How do I write a quadratic equation if I'm given the vertex and x-intercepts?

Question

I'm trying to create a parabola for a quadratic equation whose:

vertex = (1, 0.8)

x-intercepts = -1 and 3

Answer 1

First, we have to use the vertex form of a parabolic formula.

y=a(x-h)²+k, where our vertex is (h,k).

plugging in (1,0.8) for our values of h and k, we get:

y = a*(x-1)² + 0.8

to find the value of a, plug in one of your x-intercepts. Remember, and X-intercept is the value of X when Y is zero.

Let's use X = 3. if we plug in the point (3,0) into our equation, we get:

0 = a*(3-1)²+ 0.8

0 = a*4 + 0.8

subtract 0.8 from each side

-0.8 = a*4

divide both sides by 4:

a = -0.2

So our quadratic equation is: y=-0.2(x-1)² + 0.8

Which we can expand into: y= -0.2x² + 0.4x + 0.6

Let me know if you have any questions!