Question

Sketch f(x) = 5x2 - 20 labelling any intercepts.​

Answer 1

Answer:

• The graph of the function is attached below.

• The x-intercepts will be: (2, 0), (-2, 0)

• The y-intercept will be: (-20, 0)

Explanation:

Given the function

$f\left(x\right)\:=\:5x^2-\:20$

As we know that the x-intercept(s) can be obtained by setting the value y=0

so

$y=\:5x^2-\:20$

switching sides

$5x^2-20=0$

Add 20 to both sides

$5x^2-20+20=0+20$

$5x^2=20$

Dividing both sides by 5

$\frac{5x^2}{5}=\frac{20}{5}$

$x^2=4$

$\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

$x=\sqrt{4},\:x=-\sqrt{4}$

$x=2,\:x=-2$

so the x-intercepts will be: (2, 0), (-2, 0)

we also know that the y-intercept(s) can obtained by setting the value x=0

so

$y=\:5(0)^2-\:20$

$y=0-20$

$y=-20$

so the y-intercept will be: (-20, 0)

From the attached figure, all the intercepts are labeled.