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:Vertex form: f(x) = -10(x − 2)^2 + 3Standard form: y = -10x^2 + 40x - 37Step-by-step explanation:h and k are the vertex coordinatesSubstitute them in the vertex form equation: f(x) = a(x − 2)^2 + 3Calculate "a" by replacing "f(x)" with -7 and "x" with 1:-7 = a(1 − 2)^2 + 3Simplify:-7 = a(1 − 2)^2 + 3-7 = a(-1)^2 + 3-7 = a + 3-10 = aReplace a to get the final vertex form equation:f(x) = -10(x − 2)^2 + 3Convert to standard form:y = -10(x − 2)^2 + 3Expand using binomial theorem:y = -10(x^2 − 4x + 4) + 3Simplify:y = -10x^2 + 40x - 40 + 3y = -10x^2 + 40x - 37