Click on each tab to practice graphing the quadratic equations and finding the quadratic equations from the graphs.
Problem 1
Problem 2
Problem 3
Problem 4
Graph the equation \(\small\mathsf{ f(x) = \frac{1}{2}(x-1)^{2} - 5 }\).
The vertex is at (h, k) = (1, -5).
The parabola opens up and is wider than the parent function, \(\small\mathsf{ a = \frac{1}{2} < 1 }\).
It goes through the points (-1, -3) and (3, -3).
Graph the equation \(\small\mathsf{ f(x) = -2(x+3)^{2} + 5 }\).
The vertex is at (h, k) = (-3, 5).
The parabola opens down and is narrower than the parent function, \(\small\mathsf{ |a| = 2 > 1 }\).
It goes through the points (-4, 3) and (-2, 3).
Find the equation of the graph.
The vertex is at (h, k) = (2, 1).
The parabola opens up, so a > 0.
It goes through the point (1, 2).
| \(\small\mathsf{ f(x) = a(x-2)^{2} + 1 }\) |
| \(\small\mathsf{ f(1) = a(1-2)^{2} + 1 }\) |
| \(\small\mathsf{ 2 = a(-1)^{2} + 1 }\) |
| \(\small\mathsf{ 2 = 1a + 1 }\) |
| \(\small\mathsf{ a = 1 }\) |
| \(\small\mathsf{ f(x) = 1(x-2)^{2} + 1 }\) |
Find the equation of the graph.
The vertex is at (h, k) = (-3, 6).
The parabola opens down, so a < 0.
It goes through the point (-4, 4).
| \(\small\mathsf{ f(x) = a(x+3)^{2} + 6 }\) |
| \(\small\mathsf{ f(-4) = a(-4+3)^{2} + 6 }\) |
| \(\small\mathsf{ 4 = a(-1)^{2} + 6 }\) |
| \(\small\mathsf{ 4 = 1a + 6 }\) |
| \(\small\mathsf{ a = -2 }\) |
| \(\small\mathsf{ f(x) = -2(x+3)^{2} + 6 }\) |
