Question

Find the x-intercepts of the parabola with vertex (1,20) and y-intercept (0,16).

Answer 1

Answer:

Step-by-step explanation:

Since we are finding the x-intercepts, that implies that this is a parabola that opens either up or down as opposed to right or left. It would benefit us to know the equation of the parabola so we could factor it to find the roots (which are also known as the x-intercepts).

Here's what we know:

h = 1, k = 20, x = 0, and y = 20. Filling in the vertex form of a parabola is already halfway to factored, so we'll use that format as opposed to the standard form, which is

$y=ax^2+bx+c$. The vertex form is

$y=a(x-h)^2+k$ and filling in our values from above:

$16=a(0-1)^2+20$ and

$16=a(1)+20$ and

-4 = a. So the equation for the parabola is

$y=-4(x-1)^2+20$. Now set it equal to 0 and factor.

$-20=-4(x-1)^2$ and divide both sides by -4 to get:

$5=(x-1)^2$ and take the square root of both sides to get

±$\sqrt{5}=x-1$ and then add 1 to both sides to get the x-intercepts (or roots or solutions or zeros...they're all the same).

x = 1 ±√5 and you're done!