Question

What is the vertex form, f(x) = a(x − h)2 + k, for a parabola that passes through the point (1, −7) and has (2, 3) as its vertex. What is the standard form of the equation?

Answer 1

Vertex form: f(x) = -10(x − 2)^2 + 3

Standard form: y = -10x^2 + 40x - 37

Explanation:

h and k are the vertex coordinates

Substitute them in the vertex form equation:

f(x) = a(x − 2)^2 + 3

Calculate "a" by replacing "f(x)" with -7 and "x" with 1:

-7 = a(1 − 2)^2 + 3

Simplify:

-7 = a(1 − 2)^2 + 3

-7 = a(-1)^2 + 3

-7 = a + 3

-10 = a

Replace a to get the final vertex form equation:

f(x) = -10(x − 2)^2 + 3

Convert to standard form:

y = -10(x − 2)^2 + 3

Expand using binomial theorem:

y = -10(x^2 − 4x + 4) + 3

Simplify:

y = -10x^2 + 40x - 40 + 3

y = -10x^2 + 40x - 37