Graphing f (x) = ax² + bx + c Practice — Grade 8 math

Lesson 3: Graphing f (x) = ax² + bx + c — Practice Questions

1. Consider the quadratic function $f(x) = 3x^2 - 6x - 4$. Which statement correctly describes the graph of the parabola?
- A. The parabola opens upward.
- B. The parabola opens downward.
- C. The vertex is on the y-axis.
- D. The y-intercept is positive.
2. The equation for the axis of symmetry of the parabola $f(x) = 2x^2 - 8x + 5$ is $x = $ ___.
3. Find the coordinates of the vertex for the quadratic function $f(x) = -x^2 - 4x + 1$. The vertex is at the point ___.
4. What are the coordinates of the $y$-intercept for the graph of the function $f(x) = -2x^2 + 5x + 7$? Enter the point as `(x, y)`. ___
5. The graph of $f(x) = x^2 - 6x + 5$ has a $y$-intercept at $(0, 5)$. What are the coordinates of the point symmetric to the $y$-intercept across the axis of symmetry?
- A. (6, 5)
- B. (3, -4)
- C. (0, -5)
- D. (-6, 5)
6. Find the vertex of the parabola for the function $f(x) = x^2 + 6x + 5$. Enter the point as an ordered pair.
7. Find the vertex of the parabola for the function $f(x) = x^2 + 2x - 7$. Enter the point as an ordered pair.
8. Find the vertex of the parabola for $f(x) = 4x^2 - 6x - 2$. Enter your answer as an ordered pair, using fractions if necessary.
9. Find the vertex of the parabola for the function $f(x) = x^2 - 6x + 8$. Enter the point as an ordered pair.
10. A retailer who sells backpacks finds that the revenue from selling them for $x$ dollars each is given by the function $R(x) = -x^2 + 100x$. Find the selling price that will give the maximum revenue. Selling price: ___ dollars.