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:
Step 1: Apply the distributive property (FOIL) to the binomials :
Step 2: Multiply the result by :
Now, distribute the across each term:
Final answer in Standard Form:
This is the quadratic function in standard form: , where , , and .
Would you like a more detailed explanation of any step?
Additional questions for you:
- How would you solve for the roots of a quadratic equation in standard form?
- What is the significance of the coefficient in a quadratic function?
- How do you identify the vertex of a quadratic function from its standard form?
- What is the process to factor a quadratic function back into its factored form?
- 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 , where and are the coefficients from .
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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