Question

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

Answer 1

To find quadratic equations with x-intercepts at (1,0) and (-3,0) but produce different parabolas, we can use the factored form of a quadratic equation.

Step-by-step explanation:

To find quadratic equations with x-intercepts at (1,0) and (-3,0) but produce different parabolas, we can use the factored form of a quadratic equation. The factored form is given by:

f(x) = a(x - r)(x - s)

where r and s are the x-intercepts of the equation. Let's find three examples:

1. f(x) = (x - 1)(x + 3)
2. f(x) = 2(x - 1)(x + 3)
3. f(x) = 3(x - 1)(x + 3)

Each of these equations has x-intercepts at (1,0) and (-3,0), but they have different parabolas because of the coefficient a. The coefficient affects the steepness and orientation of the parabola. For example, the parabola in the first equation is steeper than the parabola in the second equation.