# What is the equation of the parabola that has a vertex at # (9, -23) # and passes through point # (35,17) #?

##### 2 Answers

We can solve this using the vertex formula,

#### Explanation:

The standard format for a parabola is

But there is also the vertex formula,

Where

So from the question, the equation would be

To find a, substitute the x and y values given:

so the formula, in vertex form, is

To find the standard form, expand the

For problems of this type, use vertex form, y = a

#### Explanation:

In vertex form, mentioned above, the vertex's coordinates are (p, q) and a point (x , y) that is on the parabola.

When finding the equation of the parabola, we have to solve for a, which influences the width and the direction of opening of the parabola.

y = a

17 = a

17 = 576a - 23

17 + 23 = 576a

So, the equation of the parabola is y =

Hopefully you understand now!