MATH SOLVE

2 months ago

Q:
# Use the parabola tool to graph the quadratic function f(x)=−12x2+7. Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

Accepted Solution

A:

First we find the vertex of parabola [tex]f(x)=-12 x^{2} +7[/tex]

The vertex of parabola is [tex]( \frac{-b}{2a},f( \frac{-b}{2a})) [/tex]

Here,

b = coefficient of x term

a = coefficient of x² term

For given parabola, b = 0 , a = -12

So,

[tex] \frac{-b}{2a}= \frac{0}{-24} =0 [/tex]

And,

[tex]f( \frac{-b}{2a} )=f(0) = -12(0)+7=7[/tex]

Thus the vertex of parabola is (0, 7)

To find another point on parabola, substitute x by 1.

[tex]f(1)=-12( 1^{2}) +7=-12+7=-5[/tex]

So the second point on parabola is (1,-5)

The plot of parabola is shown in image below:

The vertex of parabola is [tex]( \frac{-b}{2a},f( \frac{-b}{2a})) [/tex]

Here,

b = coefficient of x term

a = coefficient of x² term

For given parabola, b = 0 , a = -12

So,

[tex] \frac{-b}{2a}= \frac{0}{-24} =0 [/tex]

And,

[tex]f( \frac{-b}{2a} )=f(0) = -12(0)+7=7[/tex]

Thus the vertex of parabola is (0, 7)

To find another point on parabola, substitute x by 1.

[tex]f(1)=-12( 1^{2}) +7=-12+7=-5[/tex]

So the second point on parabola is (1,-5)

The plot of parabola is shown in image below: