Question 1124651

Find the quadratic equation function that has the given vertex and goes through the given point. Vertex(1,3), point (-2,0) f(x) =
<pre>Since the vertex of and a point on the parabola are given, we use the vertex form of a parabolic equation, or {{{matrix(1,3, f(x), "=", a(x - h)^2 + k)}}}, with (h, k) being the vertex, and the point (x, y)
{{{matrix(1,3, 0, "=", a(- 2 - 1)^2 + 3)}}} ----- Substituting y for f(x), and then 0 for y, (1, 3) for (h, k), and (- 2, 0) for (x, y) in order to determine "a."
{{{matrix(1,3, 0, "=", a(- 3)^2 + 3)}}}
0 = 9a + 3
- 3 = 9a_____{{{matrix(1,5, a, "=", - 3/9, or, - 1/3)}}}
{{{matrix(1,3, f(x), "=", a(x - h)^2 + k)}}}
{{{highlight_green(matrix(1,3, f(x), "=", (- 1/3)(x - 1)^2 + 3))}}} ------- Substituting {{{- 1/3}}} for "a," and (1, 3) for (h, k)