standar form of quadratic

Question

Write the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point. (Let x be the independent variable and y be the dependent variable.)

Vertex:	− 7
2
, 0

;

point:	− 9
2
, − 4
5

Answer 1

if the vertex is (2,0)

the quadratic is

y =a(x-2)^2

plug in the coordinates of the other point to solve for a

general formula is

y =a(x-h)^2 +k where (h,k) is the vertex

for (2,0) h=2 and k=0

if the other point is (-7,162)

then

162 =a(-7-2)^2 = 81a

a = 162/81 =2

and the quadratic is

y=2(x-2)^2