How do you find the x and y intercepts for f(x)=4x^2-36?

May 23, 2018

$\text{x-intercepts "=+-3," y-intercept } = - 36$

Explanation:

$\text{to find the intercepts, that is where the graph crosses}$
$\text{the x and y axes}$

• " let x = 0, in the equation for y-intercept"

• " let y = 0, in the equation for x-intercepts"

$x = 0 \to y = 0 - 36 = - 36 \leftarrow \textcolor{red}{\text{y-intercept}}$

$y = 0 \to 4 {x}^{2} - 36 = 0$

$\text{add 36 to both sides and divide by 4}$

$4 {x}^{2} = 36 \Rightarrow {x}^{2} = 9$

$\textcolor{b l u e}{\text{take the square root of both sides}}$

$x = \pm \sqrt{9} \leftarrow \textcolor{b l u e}{\text{note plus or minus}}$

$x = \pm 3 \leftarrow \textcolor{red}{\text{x-intercepts}}$