| Write an equation for the parabola whose vertex is at (-3, -2) and passes through (-1, 8). |
|---|
Step 1 |
The
vertex of the parabola is at (-3, -2) so h
= -3 and k = -2 . Since (-1, 8) is a point on the graph of the parabola, let x = -1 and y = 8 . Substitute these values into the vertex form of the equation and solve for a. |
|---|---|
Show Me |
y = a(x - h)^2 + k \quad \quad Vertex
Form. 8 = a[-1 - (-3)]^2 - 2 \quad \quad \quad Substitute 8 for y, -1 for x, -3 for h, and -2 for k. |
Step 2 |
Simplify
the expression . |
|---|---|
Show Me |
8 = a(4) - 2 |
Step 3 |
Add
2 to each side . |
|---|---|
Show Me |
10 = a(4) |
Step 4 |
Divide
each side by 4 . |
|---|---|
Show Me |
\frac{10}{4} = a \frac{5}{2} = a |
Step 5 |
Write
the equation in vertex form. |
|---|---|
Show Me |
y = \frac{5}{2}(x + 3)^2 - 2 |
Step 6 |
Check. A graph of \quad y = \frac{5}{2}(x + 3)^2 - 2 \quad verifies that the parabola passes through the point (-1, 8). |
|---|---|
Show Me |
|