About Lesson
2.4 Graph and Nature of Quadratic Equation 一元二次函数的图像及性质
Sketch the following functions, state also their symmetric axis, extreme point, domain and range.
画出下列函数的图像,并写出它们的对称轴,顶点,定义域和值域。
[1]
Answer :
x = 1, (1, 1), D = R, R = [1,
)
![Rendered by QuickLaTeX.com \infty](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-5c9307a0dc01eff42f781692d412b225_l3.png)
[2]
Answer :
x =
, (
, 10
), D = R, R = (
, 10
]
![](data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20width%3D%22799%22%20height%3D%22595%22%20viewBox%3D%220%200%20799%20595%22%3E%3Cfilter%20id%3D%22b%22%3E%3CfeGaussianBlur%20stdDeviation%3D%2212%22%20%2F%3E%3C%2Ffilter%3E%3Cpath%20fill%3D%22%23fff%22%20d%3D%22M0%200h799v593H0z%22%2F%3E%3Cg%20filter%3D%22url(%23b)%22%20transform%3D%22translate(1.6%201.6)%20scale(3.1211)%22%3E%3Cellipse%20fill%3D%22%23fff%22%20fill-opacity%3D%22.5%22%20cx%3D%2262%22%20cy%3D%2223%22%20rx%3D%223%22%20ry%3D%2219%22%2F%3E%3Cpath%20stroke%3D%22%23fff%22%20stroke-opacity%3D%22.5%22%20fill%3D%22none%22%20d%3D%22M155.8%20123.8q9.7-13.8%206.7-27.8%22%20stroke-width%3D%22.5%22%2F%3E%3Cpath%20fill%3D%22%23fff%22%20fill-opacity%3D%22.5%22%20d%3D%22M102%208h27v15h-27zM7.6%20153l-8.5-7.6-6%2019.4%2010-20z%22%2F%3E%3C%2Fg%3E%3C%2Fsvg%3E)
![Rendered by QuickLaTeX.com 1\frac{2}{3}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-5346c6a51c97b228d4927760e3fbd9b0_l3.png)
![Rendered by QuickLaTeX.com 1\frac{2}{3}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-5346c6a51c97b228d4927760e3fbd9b0_l3.png)
![Rendered by QuickLaTeX.com 1\frac{1}{9}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-c271f577745dcbcbe626ef7e6d4b3115_l3.png)
![Rendered by QuickLaTeX.com -\infty](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-7b98d4ae5e1d3f23975f1017a23be92f_l3.png)
![Rendered by QuickLaTeX.com \frac{1}{9}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-b89f1511ebad7b917e28dc1c52c014b9_l3.png)
![](https://learn-ondemand.com/wp-content/uploads/2021/07/C2.4-Q2-GRAPH.jpg)
[3] ![Rendered by QuickLaTeX.com y = 2x^2 +5x - 3](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-cdb0eeded6dc9c4522c682bcf61e794c_l3.png)
![Rendered by QuickLaTeX.com y = 2x^2 +5x - 3](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-cdb0eeded6dc9c4522c682bcf61e794c_l3.png)
Answer :
x =
, (
,
), D = R, R = [
,
)
![](data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20width%3D%22567%22%20height%3D%22594%22%20viewBox%3D%220%200%20567%20594%22%3E%3Cfilter%20id%3D%22b%22%3E%3CfeGaussianBlur%20stdDeviation%3D%2212%22%20%2F%3E%3C%2Ffilter%3E%3Cpath%20fill%3D%22%23fefefe%22%20d%3D%22M0%200h566v594H0z%22%2F%3E%3Cg%20filter%3D%22url(%23b)%22%20transform%3D%22translate(1.2%201.2)%20scale(2.32031)%22%20fill-opacity%3D%22.5%22%3E%3Cellipse%20fill%3D%22%23ccc%22%20rx%3D%221%22%20ry%3D%221%22%20transform%3D%22rotate(-1.3%204527.2%20-8207.7)%20scale(11.90308%2024.444)%22%2F%3E%3Cellipse%20fill%3D%22%23fff%22%20cx%3D%2280%22%20cy%3D%22161%22%20rx%3D%22103%22%20ry%3D%22103%22%2F%3E%3Cellipse%20fill%3D%22%23fff%22%20rx%3D%221%22%20ry%3D%221%22%20transform%3D%22matrix(-46.06106%20169.38162%20-58.89795%20-16.0165%20243%20139.8)%22%2F%3E%3Cellipse%20fill%3D%22%23dcdcdc%22%20cx%3D%22179%22%20cy%3D%2297%22%20rx%3D%228%22%20ry%3D%2227%22%2F%3E%3C%2Fg%3E%3C%2Fsvg%3E)
![Rendered by QuickLaTeX.com -1\frac{1}{4}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-1c484ea18deeeba8831487493407900f_l3.png)
![Rendered by QuickLaTeX.com -1\frac{1}{4}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-1c484ea18deeeba8831487493407900f_l3.png)
![Rendered by QuickLaTeX.com -6\frac{1}{8}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-f6553eb41e39e903f6e3fe7dd876cd73_l3.png)
![Rendered by QuickLaTeX.com -6\frac{1}{8}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-f6553eb41e39e903f6e3fe7dd876cd73_l3.png)
![Rendered by QuickLaTeX.com \infty](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-5c9307a0dc01eff42f781692d412b225_l3.png)
![](https://learn-ondemand.com/wp-content/uploads/2021/07/C2.4-Q3-GRAPH.jpg)
[4] ![Rendered by QuickLaTeX.com y = 2x^2 - 3x + 2](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-8c5e0b41b4fde821bfa3e945b5fcdc19_l3.png)
![Rendered by QuickLaTeX.com y = 2x^2 - 3x + 2](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-8c5e0b41b4fde821bfa3e945b5fcdc19_l3.png)
Answer :
x =
, (
,
), D = R, R = [
,
)
![](data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20width%3D%22686%22%20height%3D%22605%22%20viewBox%3D%220%200%20686%20605%22%3E%3Cfilter%20id%3D%22c%22%3E%3CfeGaussianBlur%20stdDeviation%3D%2255%22%20%2F%3E%3C%2Ffilter%3E%3Cpath%20fill%3D%22%23fefefe%22%20d%3D%22M0%200h686v602H0z%22%2F%3E%3Cg%20filter%3D%27url(%23c)%27%20fill-opacity%3D%27.5%27%3E%3Cellipse%20fill%3D%22%23cecece%22%20fill-opacity%3D%22.5%22%20rx%3D%221%22%20ry%3D%221%22%20transform%3D%22rotate(69.3%20-161.1%20463.8)%20scale(50.8482%2057.97738)%22%2F%3E%3Cpath%20fill%3D%22%23dedede%22%20fill-opacity%3D%22.5%22%20d%3D%22M304%20518.7l102-86.4L287%20386l-5.8%2069.8z%22%2F%3E%3Cpath%20fill%3D%22%23fff%22%20fill-opacity%3D%22.5%22%20d%3D%22M690.7-41.5L-41.5%208.3l372%20406.7%20397%2067.6z%22%2F%3E%3Cpath%20fill%3D%22%23fff%22%20fill-opacity%3D%22.5%22%20d%3D%22M1.3%201.3h286.8v603H1.3z%22%2F%3E%3C%2Fg%3E%3C%2Fsvg%3E)
![Rendered by QuickLaTeX.com \frac{3}{4}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-65fd0de1893509d9cf44e15ddea9a46e_l3.png)
![Rendered by QuickLaTeX.com \frac{3}{4}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-65fd0de1893509d9cf44e15ddea9a46e_l3.png)
![Rendered by QuickLaTeX.com \frac{7}{8}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-fb0ee9cf9ddfc61bce5ece53ffce2a1d_l3.png)
![Rendered by QuickLaTeX.com \frac{7}{8}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-fb0ee9cf9ddfc61bce5ece53ffce2a1d_l3.png)
![Rendered by QuickLaTeX.com \infty](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-5c9307a0dc01eff42f781692d412b225_l3.png)
![](https://learn-ondemand.com/wp-content/uploads/2021/07/C2.4-Q4-GRAPH.jpg)
[5] ![Rendered by QuickLaTeX.com y = 1 - 3x - x^2](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-15820b0b654e3bbb48fafaa5219811d4_l3.png)
![Rendered by QuickLaTeX.com y = 1 - 3x - x^2](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-15820b0b654e3bbb48fafaa5219811d4_l3.png)
Answer :
x =
, (
,
), D = R, R = (
,
]
![](data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20width%3D%22554%22%20height%3D%22694%22%20viewBox%3D%220%200%20554%20694%22%3E%3Cfilter%20id%3D%22c%22%3E%3CfeGaussianBlur%20stdDeviation%3D%2255%22%20%2F%3E%3C%2Ffilter%3E%3Cpath%20fill%3D%22%23fefefe%22%20d%3D%22M0%200h553v694H0z%22%2F%3E%3Cg%20filter%3D%27url(%23c)%27%20fill-opacity%3D%27.5%27%3E%3Cellipse%20fill%3D%22%23cdcdcd%22%20fill-opacity%3D%22.5%22%20rx%3D%221%22%20ry%3D%221%22%20transform%3D%22matrix(21.8228%20.32446%20-.79437%2053.42913%20408.5%20389.1)%22%2F%3E%3Cellipse%20fill%3D%22%23fff%22%20fill-opacity%3D%22.5%22%20rx%3D%221%22%20ry%3D%221%22%20transform%3D%22matrix(-206.99716%20-73.30154%20183.70072%20-518.75484%20172.4%20335.4)%22%2F%3E%3Cpath%20fill%3D%22%23dcdcdc%22%20fill-opacity%3D%22.5%22%20d%3D%22M402.6%20456.8l-14-69.7%2017.5-41%2036%2045.5z%22%2F%3E%3Cellipse%20fill%3D%22%23fff%22%20fill-opacity%3D%22.5%22%20rx%3D%221%22%20ry%3D%221%22%20transform%3D%22matrix(112.32015%205.03778%20-9.60357%20214.1173%20506%20205.2)%22%2F%3E%3C%2Fg%3E%3C%2Fsvg%3E)
![Rendered by QuickLaTeX.com -1\frac{1}{2}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-7aa421ac22e3fbcdeed0fa6e08af5c70_l3.png)
![Rendered by QuickLaTeX.com -1\frac{1}{2}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-7aa421ac22e3fbcdeed0fa6e08af5c70_l3.png)
![Rendered by QuickLaTeX.com 3\frac{1}{4}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-ca7efefd1c79a5ffab4f9e2d3c1b2c2d_l3.png)
![Rendered by QuickLaTeX.com -\infty](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-76241bde5133294fe4fd13de97a075ce_l3.png)
![Rendered by QuickLaTeX.com 3\frac{1}{4}](https://learn-ondemand.com/wp-content/ql-cache/quicklatex.com-ca7efefd1c79a5ffab4f9e2d3c1b2c2d_l3.png)
![](https://learn-ondemand.com/wp-content/uploads/2021/07/C2.4-Q5-GRAPH.jpg)