How do you find the x and y intercepts for f(x) = (x-3)^2 + 17?

Aug 2, 2017

Answer:

$\text{y-intercept "=26" no x-intercepts}$

Explanation:

$\text{to find the intercepts}$

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

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

$x = 0 \to y = {\left(- 3\right)}^{2} + 17 = 26 \leftarrow \textcolor{red}{\text{ y-intercept}}$

$y = 0 \to {\left(x - 3\right)}^{2} + 17 = 0$

$\Rightarrow {\left(x - 3\right)}^{2} = - 17$

$\forall x \in \mathbb{R} \textcolor{w h i t e}{x} {\left(x - 3\right)}^{2} \ge 0$

$\Rightarrow \text{ there are no x-intercepts}$
graph{(x-3)^2+17 [-80, 80, -40, 40]}