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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

Consider a parabola that has a y-intercept at (0, -21), x-intercepts at (-7, 0) and-example-1
User Copeg
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1 Answer

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Final answer:

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

User Shogg
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