# What are the x– and y–intercepts of the quadratic equation y = 2x^2 – 8x + 6?

Mar 24, 2018

y-intercept: $\left(0 , 6\right)$
x-intercepts: $\left(1 , 0\right)$ and $\left(3 , 0\right)$

#### Explanation:

1) To find the y-intercept, set $x = 0$ and solve for $y$:
$y = 2 {x}^{2} - 8 x + 6$
$y = 2 {\left(0\right)}^{2} - 8 \left(0\right) + 6$
$y = 0 - 0 + 6$
$y = 6$
y-intercept: $\left(0 , 6\right)$

2) To find the x-intercepts, set $y = 0$ and solve for $x$:
$y = 2 {x}^{2} - 8 x + 6$
$\left(0\right) = 2 {x}^{2} - 8 x + 6$
$0 = {x}^{2} - 4 x + 3$
$0 = \left(x - 1\right) \left(x - 3\right)$
$0 = \left(x - 1\right)$ and $0 = \left(x - 3\right)$
$1 = x$ and $3 = x$
x-intercepts: $\left(1 , 0\right)$ and $\left(3 , 0\right)$