Question

2.1 & 2.2 Assessment: Vertex & Standard Form of Quadratic Functions

What is the equation, written in vertex form, of a parabola with a vertex of (1, -9) that
passes through the point (2, -7)?



The equation of the parabola in vertex form is _______________

Answer 1

y = 2(x - 1)^2 - 9

Explanation:

The vertex form of a parabola is y = a(x - h)^2 + k

(h, k) is the vertex, aka (1, -9)

(x, y) is the point that is passed through aka (2, -7)

Using this, we can substitute these values into the equation.

First, let's work with the vertex

We know that h = 1 and k = -9: y = a(x - 1)^2 - 9

Now, let's substitute in the point that was given: -7 = a(2 - 1)^2 - 9

Now, we can find the a-value by simplifying: -7 = a - 9 --> a = 2

Finally, we can make the equation by taking our equation that we made with the vertex but just putting the a-value in since we know it.

y = 2(x - 1)^2 - 9 is the equation of the parabola in vertex form

I hope this helps! Let me know if it is wrong