equation of parabola if axis of symmetry x=-2; passes through (0,7)&(-3,-2)

Question

we have to determine an equation with only the given information:

- axis of symmetry is x = -2

- passes through point (0,7)

- passes through point (-3,-2)

Answer 1

So, since the x-value of the vertex is -2 (corresponds to an axis of symmetry of x = -2) then 1) we know the parabola is upright and takes the form of y = a(x + 2)² + k. Plugging in the two points, we get two equations in two unknowns:

1) 7 = a(0 + 2)² + k

2) -2 = a(-3 + 2)² + k

Simplifying, we get:

1) 4a + k = 7

2) a + k = -2

Subtracting the two equations gives us:

3a = 9 or a = 3

Plugging that into equation 2, we get 3 + k = -2 or k = -5, so the equation becomes:

y = 3(x + 2)² - 5

If, you want it in standard form, multiply it out:

y = 3(x² + 4x + 4) - 5

y = 3x² + 12x + 12 - 5

y = 3x² + 12x + 7