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:
