Question

Use the x-intercepts and given point on each parabola to write the equation of the quadratic function in intercept form: f(x)= a(x-x1) (x-x2)

x intercepts are (-5,0) (-3,0)
the other points are (-6,-6)

Answer 1

To write the equation of a quadratic function using x-intercepts and a point, substitute the intercepts into the equation and solve for the remaining variable. The given equation in intercept form is f(x) = -1/3(x + 5)(x + 3).

Step-by-step explanation:

To write the equation of a quadratic function in intercept form, we need to use the x-intercepts and a given point on the parabola. Given that the x-intercepts are (-5,0) and (-3,0), we can start by substituting these values into the equation.

Let's use the point (-6,-6) to find the value of 'a' in the equation. Substituting these values into the quadratic function, we get:

f(x) = a(x - x1)(x - x2)

f(-6) = a(-6 - (-5))(-6 - (-3)) = -6.

By solving the equation, we find that 'a' equals -1/3. Therefore, the equation of the quadratic function in intercept form is:

f(x) = -1/3(x + 5)(x + 3).