Since the graph indicates the vertex, use the Vertex Form. Slot (h,k) and (x,y) into the Vertex Form to solve for a. Then, substitute a, h and k back to the main formula to form an equation.
First, label values from the graph
Note that the vertex is at (-2,3)
h
=
-2
from vertex
k
=
3
from vertex
x
=
-5
x intercept
y
=
0
value of y at x intercept
Now, slot these values into the Vertex Form and solve for a
y
=
a(x−h)2+k
Vertex Form
0
=
a(−5−(−2))2+3
Substitute values
0
=
a(-3)2+3
0
=
9a+3
9a+3
=
0
9a+3-3
=
0-3
Subtract 3 from both sides
9a÷9
=
-3÷9
Divide both sides by 9
a
=
-39
a
=
-13
Simplify
Finally, substitute a, h and k into the Vertex Form
Since the graph indicates the vertex, use the Vertex Form. Slot (h,k) and (x,y) into the Vertex Form to solve for a. Then, substitute a, h and k back to the main formula to form an equation.
First, label values from the graph
h
=
3
from vertex
k
=
2
from vertex
x
=
4
from given point
y
=
1
from given point
Now, slot these values into the Vertex Form and solve for a
y
=
a(x−h)2+k
Vertex Form
1
=
a(4−3)2+2
Substitute values
1
=
a(1)2+2
1
=
a+2
a+2
=
1
a+2-2
=
1-2
Subtract 2 from both sides
a
=
-1
Finally, substitute a, h and k into the Vertex Form