Question

In the following exercises, find thex- intercept andy- intercept.

$y=16x^2-8x+1$

Short answer

x- intercept is the point$(\frac{1}{4},0)$and y- intercept is the point$(0,1)$.

Step-by-step solution

Given information

The given expression is:$y=16x^2-8x+1$

Determine the x- intercept.

set $y=0$and solve for x.

$$\begin{gathered} 0=16x^2-8x+1 \\ 16x^2-8x+1=0 \end{gathered}$$

Solve the equation using factoring.

$(4x-1)(4x-1)=0$

$4x-1=0$ or $4x-1=0$

$x=\frac{1}{4}$ or $x=\frac{1}{4}$

The result gives that when $y=0$, then $x=\frac{1}{4}$.

x- intercept is the point$(\frac{1}{4},0)$

Determine the y- intercept.

Substitute $x=0$and evaluate $y\left(0\right)$.

$$\begin{gathered} y\left(0\right)=0+0+1 \\ =1 \end{gathered}$$

y- intercept is the point$(0,1)$.