Question

Find the x-intercepts of the parabola with vertex (1, -9) and y intercept at (0, -6).

Answer 1

• Vertex Form: y = a(x - h)^2 + k, with (h,k) as the vertex.

So firstly, plug the vertex into the vertex form: $y=a(x-1)^2-9$

Next, we first need to solve for a. Plug (0,-6) into the equation to solve for a as such:

$-6=a(0-1)^2-9\\-6=a(-1)^2-9\\-6=a-9\\3=a$

Now we know that our equation is y = 3(x - 1)^2 - 9.

Now to solve for the zeros (x-intercepts). Set y to 0 and add 9 to both sides of the equation: $9=3(x-1)^2$

Next, divide both sides by 3: $3=(x-1)^2$

Next, square root both sides: $\pm\sqrt{3}=x-1$

Next, add 1 to both sides: $1\pm\sqrt{3}=x\\2.73,-0.73=x$

Your x-intercepts are (-0.73,0) and (2.73,0), or B.