Question

A parabola has a vertex of (3, -7) and passes through the point (15, 29). When the equation of the parabola is written in the form y = a(x - h)² + k, what is the value of a?

Answer 1

To find the value of a, substitute the vertex and another point into the vertex form of the parabola equation, then solve for a.

Step-by-step explanation:

To find the value of a, we can use the vertex form of a parabola, which is y = a(x - h)² + k. The vertex of the parabola is given as (3, -7), so the equation is y = a(x - 3)² - 7. We can substitute the coordinates of the other point, (15, 29), into the equation to solve for a.

Plugging in the values for x and y, we get 29 = a(15 - 3)² - 7. Simplifying, we have 29 = a(12)² - 7. Expanding, we get 29 = a(144) - 7. Combining like terms, we have 29 = 144a - 7. Adding 7 to both sides, we get 36 = 144a. Finally, dividing both sides by 144, we find that a = 0.25.