Question

The equation of a parabola in vertex form is y = a(x + 2)² + 5. If the parabola passes through the point (-4, 21), what is the value of a?

a) 3
b) 4
c) 5
d) 6

Answer 1

To find the value of a in the equation of a parabola in vertex form, you can substitute the coordinates of a point that the parabola passes through into the equation and solve for a. In this case, the value of a is 4.

Step-by-step explanation:

The equation of a parabola in vertex form is y = a(x + 2)² + 5. To find the value of a, we can substitute the coordinates of the point (-4, 21) into the equation and solve for a. So, we have 21 = a(-4 + 2)² + 5. Simplifying this equation, we get 21 = a(2)² + 5, which becomes 21 = 4a + 5. Subtracting 5 from both sides gives us 16 = 4a. Finally, dividing both sides by 4, we find that a = 4.