Question

The vertex of this parabola is at (2, -4). When the y-value is -1, the x-value is 3. What is the coefficient of the squared term in the parabola's equation?

Answer 1

3

Explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (2, - 4) , thus

y = a(x - 2)² - 4

To find a substitute (3, - 1 ) into the equation

- 1 = a(3 - 2)² - 4 ( add 4 to both sides )

3 = a

Thus

y = 3(x - 2)2 - 4 ← equation in vertex form

= 3(x² - 4x + 4) + 4

= 3x² - 12x + 12 + 4

= 3x² - 12x + 16 ← equation in standard form

with coefficient of x² term = 3