Question

Consider a parabola that has a y-intercept at (0, -21), x-intercepts

at (-7, 0) and (3, 0), and a vertex at (-2,-25). The quadratic
equation for this parabola could be written in three different
forms. Fill in the blanks below to complete each form (*make sure
to include a plus or minus sign with each number and DO NOT type
a space between the symbol and the number).
Factored form: y = (x
__)(x
Vertex form: y = (x
Standard form: y = x² + 4x

Answer 1

The quadratic equation for a parabola with specified y-intercept, x-intercepts, and vertex is expressed in factored form as y = (x+7)(x-3), in vertex form as y = (x+2)^2-25, and the standard form is completed correctly as y = x² + 4x - 21.

Step-by-step explanation:

The quadratic equation for a parabola with a y-intercept at (0, -21), x-intercepts at (-7, 0) and (3, 0), and a vertex at (-2,-25) can be written in different forms. Given the information, the factored form, vertex form, and standard form of the equation are as follows:

• Factored form: y = (x + 7)(x - 3)
• Vertex form: y = (x + 2)^2 - 25
• Standard form: y = x² + 4x - 21

Now, let's fill in the blanks in the forms provided in the question using the given intercepts and vertex:

• Factored form: y = (x+7)(x-3)
• Vertex form: y = (x+2)^2-25
• Standard form was already filled correctly as y = x² + 4x-21