Characteristics of Parabolas

Characteristics of Parabolas

Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. What is the name of the highest or lowest point on a parabola?

2. If the leading coefficient (a) of a quadratic equation is negative, in which direction does the parabola open?

3. The vertical line that passes through the vertex of a parabola and divides it into two symmetrical halves is called the  .

4. The x-intercepts of a parabola are also known as the   or   of the quadratic function.

5. For the quadratic function y = x² - 4x + 3, find the coordinates of the vertex and the equation of the axis of symmetry.

6. Determine the x-intercepts and y-intercept for the parabola defined by the equation y = x² + 2x - 8.

7. For the parabola y = -x² + 6x - 5:

a) Find the vertex.

b) Find the axis of symmetry.

c) Find the y-intercept.

d) Find the x-intercepts.

e) Sketch the parabola on the graph below, labeling the vertex and intercepts.

8. A parabola can have three x-intercepts.

9. The discriminant of a quadratic equation (b² - 4ac) can tell you the number of x-intercepts a parabola has.