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Home > A2C > Chapter 4 > Lesson 4.1.3 > Problem 4-43

4-43.
  1. Make predictions about how many places the graph of each equation below will touch the x-axis. You may first want to rewrite some of the equations in a more useful form. Homework Help ✎

    1. y = (x − 2)(x − 3)

    2. y = (x + 1)2

    3. y = x2 + 6x + 9

    4. y = x2 + 7x +10

    5. y = x2 + 6x + 8

    6. y = −x2 − 4x − 4

    7. Check your predictions with your calculator.

    8. Write a clear explanation describing how you can tell whether the equation of a parabola will touch the x-axis at only one point.

How many x-intercepts will this equation have?

Factor the right side in order to find the intercepts.

Look at parts (a) through (d).

See part (a).

Look at parts (a) through (c). Remember to factor first to find the x-intercepts.

Look at parts (a) through (d). Remember to factor −1 out.

What is true about all of the equations where the parabola touches the x-axis at only one point?