Question

the vertex of this parabola is at (4, -3). when the x-value is 5, the y-value is -6. what is the coefficient of the squared expression in the parabola's equation?*sorry edited now

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 ) = (4, - 3 ) , then

y = a(x - 4)² - 3

to find a substitute x = 5, y = - 6 into the equation

- 6 = a(5 - 4)² - 3 ( add 3 to both sides )

- 3 = a(1)² = a

y = - 3(x - 4)² - 3 ← expand factor using FOIL

y = - 3(x² - 8x + 16) - 3

= - 3x² + 24x - 48 - 3

= - 3x² - 24x - 51 ← in standard form

coefficient of the x² term is - 3