Question

Write an equation for the quadratic function graphed below

Answer 1

Answer:

y = $\frac{1}{4}$ x² + $\frac{1}{2}$ x - $\frac{15}{4}$

Step-by-step explanation:

The equation of a quadratic function in vertex form is

y = a(x - h)² + k

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

From the graph

vertex = (- 1, - 4 ) , then

y = a(x - (- 1) )² - 4 , that is

y = a(x + 1)² - 4

To find a, substitute the coordinates of any other point that lies on the graph into the equation.

using the point (- 3, - 3 ) for x and y in the equation

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

1 = a(- 2)² = 4a ( divide both sides by 4 )

$\frac{1}{4}$ = a

y = $\frac{1}{4}$ (x + 1)² - 4 ← equation in vertex form

Expand (x + 1)² using FOIL

y = $\frac{1}{4}$ (x² + 2x + 1) - 4 ← distribute parenthesis by $\frac{1}{4}$

y = $\frac{1}{4}$ x² + $\frac{2}{4}$ x + $\frac{1}{4}$ - $\frac{16}{4}$ ( simplify )

y = $\frac{1}{4}$ x² + $\frac{1}{2}$ x - $\frac{15}{4}$ ← eqation in standard form