Use the vertex (h,k) and a point on the graph (x,y) to find the equation of each quadratic function in standard form.

Question

h,k= 5,1

x,y= -8,8

Answer 1

since you are given the vertex, then you should use the vertex form

y=a(x-h)²+k

given vertex (5,1) which represents (h,k), our equation would be

y=a(x-5)²+1

next, we're going to use the given pt (-8, 8) in our equation to solve for a.

8=a(-8-5)²+1

8=a(-13)²+1

..... a=7/169

the equation in vertex form would be

y=7/169(x-5)²+1

for standard form just expand and combine like terms.

Answer 2

Start with the standard for of the equation and the vertex. Use the vertex to populate h and k.

F(x) = a(x-h)²+k Vertex: (5,1)

F(x) = a(x-5)²+1 Now use the point. (-8,8) and plug those in for x and y.

8= a((-8)-5)²+1 Now solve for a

8= a(-13)²+1 Simplify the parenthesis

8= 169a+1 Subtract 1 from both sides

7=169a Divide both sides by 169

7/169=a

Now, bring everything together for the equation

F(x) = 7/169(x-5)²+1