Write the equation of the quadratic that has a vertex of (-3,-1) and goes through the point (-4,2)

Answer 1

Vertex form of a quadratic:

y = a (x - h)² + k

In this case, the vertex is:

(h, k) = (-3, -1)

And, the point is:

(x, y) = (-4, 2)

To find "a", we substitute the vertex and the point in the formula:

2 = a ((-4) - (-3))² + (-1)

2 = a (-4 + 3)² - 1

2 = a (-1)² -1

2 = a (1) - 1

2 = a - 1

2 + 1 = a

a = 3

Equation for the quadratic in Vertex Form:

y = 3 (x - (-3))² + (-1)

y = 3 (x + 3)² - 1

To find the equation of the quadratic in Standard Form, we solve the vertex form:

y = 3 (x + 3)² - 1

y = 3 (x² + 6x + 9) - 1

y = 3x² + 18x + 27 - 1

y = 3x² + 18x + 26

Equation of the quadratic:

Vertex form: y = 3 (x + 3)² - 1

Standard form: y = 3x² + 18x + 26

Answer 2