Question

Give 3 examples of quadratic equations that have x-intercepts at (1, 0) and (-3, 0) but produce a different parabola.

A) x² - 2x - 3 = 0
B) 2x² - 5x + 3 = 0
C) -x² + 2x + 3 = 0
D) x² + 4x + 3 = 0

Answer 1

Three examples of quadratic equations with x-intercepts at (1, 0) and (-3, 0) are x² - 2x - 3 = 0, 2x² - 5x + 3 = 0, and x² + 4x + 3 = 0.

Step-by-step explanation:

In order to find three examples of quadratic equations with x-intercepts at (1, 0) and (-3, 0) that produce different parabolas, we need to create equations using the factored form of a quadratic equation. The factored form is given by (x - a)(x - b) = 0, where a and b are the x-intercepts. Using this information, we can create the following equations:

1. x² - 2x - 3 = 0
   This equation has x-intercepts at (1, 0) and (-3, 0), and its graph opens upwards.
2. 2x² - 5x + 3 = 0
   This equation also has x-intercepts at (1, 0) and (-3, 0), but its graph opens upwards and is narrower than the first equation.
3. x² + 4x + 3 = 0
   This equation has x-intercepts at (1, 0) and (-3, 0), and its graph opens upwards and is wider than the first equation.