Answer:
Vertex form: f(x) = -10(x − 2)^2 + 3
Standard form: y = -10x^2 + 40x - 37
Step-by-step 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
