Question

Create a quadratic equation that has a vertex of (3,4) and passes through the point (6,-3). Write your answer in vertex form:

f(x) = A (x + B)^2 + C
a) A = 1, B = -3, C = 4
b) A = 1, B = 3, C = 4
c) A = -1, B = 3, C = 4
d) A = -1, B = -3, C = 4

Answer 1

To create a quadratic equation with a given vertex and a point, we can use the vertex form of a quadratic equation.

Step-by-step explanation:

To create a quadratic equation that has a vertex of (3,4) and passes through the point (6,-3), we can use the vertex form of a quadratic equation: f(x) = A(x - h)^2 + k, where (h,k) is the vertex. Substituting the given vertex values, we have f(x) = A(x - 3)^2 + 4. To find the value of A, we can substitute the coordinates of the given point (6,-3) into the equation. Plugging in these values, we get -3 = A(6 - 3)^2 + 4. Solving this equation, we find A = -1. Therefore, the quadratic equation in vertex form is f(x) = -1(x - 3)^2 + 4.