Practice identifying key features of quadratic functions, graphing parabolas, and solving quadratic equations.
Read each problem carefully. Show your work and explain your reasoning when needed.
Graphing, analyzing, and solving quadratic relationships
Math - Grade 9-12
- 1
Find the vertex of the quadratic function y = x^2 - 6x + 5.
- 2
Determine whether the parabola y = -2x^2 + 8x - 1 opens upward or downward. Then state the axis of symmetry.
- 3
Write the quadratic function in standard form that has x-intercepts at x = 1 and x = 5 and passes through the point (2, -3).
- 4
Solve the equation x^2 + 7x + 12 = 0 by factoring.
- 5
Find the y-intercept of the function y = 3x^2 - 2x + 7.
- 6
A ball is thrown upward, and its height is modeled by h(t) = -16t^2 + 48t + 5. Find the maximum height of the ball.
- 7
Convert y = x^2 + 4x - 1 into vertex form.
- 8
State the domain and range of the function y = (x - 1)^2 + 6.
- 9
Find the zeros of y = x^2 - 9.
- 10
A quadratic function has vertex (4, -2) and opens upward. Write one possible equation in vertex form.
- 11
Solve x^2 - 4x - 5 = 0 using the quadratic formula.
- 12
For the function y = -x^2 + 6x - 8, find the vertex and the maximum value.
- 13
Graphing question: Describe how the graph of y = (x + 1)^2 - 3 is related to the graph of y = x^2.
- 14
Find the axis of symmetry and x-intercepts of y = x^2 - 2x - 8.
- 15
A rectangular garden has a length that is 3 feet more than its width. Its area is 54 square feet. Write and solve a quadratic equation to find the dimensions.