Math Problem Statement

Re-write the quadratic function below in Standard Form.

y, equals, minus, 7, left parenthesis, x, plus, 4, right parenthesis, left parenthesis, x, plus, 2, right parenthesis

y=

−7(x+4)(x+2)

Solution

To rewrite the given quadratic function in standard form, we need to expand and simplify the expression:

The given function is:

y=7(x+4)(x+2)y = -7(x + 4)(x + 2)

Step 1: Apply the distributive property (FOIL) to the binomials (x+4)(x+2)(x + 4)(x + 2):

(x+4)(x+2)=x2+2x+4x+8=x2+6x+8(x + 4)(x + 2) = x^2 + 2x + 4x + 8 = x^2 + 6x + 8

Step 2: Multiply the result by 7-7:

y=7(x2+6x+8)y = -7(x^2 + 6x + 8)

Now, distribute the 7-7 across each term:

y=7x242x56y = -7x^2 - 42x - 56

Final answer in Standard Form:

y=7x242x56y = -7x^2 - 42x - 56

This is the quadratic function in standard form: y=ax2+bx+cy = ax^2 + bx + c, where a=7a = -7, b=42b = -42, and c=56c = -56.


Would you like a more detailed explanation of any step?

Additional questions for you:

  1. How would you solve for the roots of a quadratic equation in standard form?
  2. What is the significance of the coefficient aa in a quadratic function?
  3. How do you identify the vertex of a quadratic function from its standard form?
  4. What is the process to factor a quadratic function back into its factored form?
  5. Can you determine the axis of symmetry for this quadratic?

Tip:

To quickly find the axis of symmetry for a quadratic function in standard form, use the formula x=b2ax = -\frac{b}{2a}, where aa and bb are the coefficients from y=ax2+bx+cy = ax^2 + bx + c.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations
Factoring
Standard Form of a Quadratic Function

Formulas

Distributive property (FOIL)
Standard form of a quadratic function y = ax^2 + bx + c

Theorems

Quadratic expansion
Factoring and expansion

Suitable Grade Level

Grades 8-10