Converting Vertex Form To Standard Form
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This document provides a 6-step process for converting a quadratic expression from vertex form to standard form: 1) Rewrite the binomial squared as two binomials, 2) FOIL the two binomials off to the side, 3) Combine like terms, 4) Replace the binomials with the new trinomial using parentheses, 5) Distribute any monomial to the trinomial, and 6) Combine like terms to obtain the standard form expression. Additional examples are provided to demonstrate the process.
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Okay, let's think through this with the new information:
* The equation modeling the height is: h = -16t^2 + vt + c
* The initial height (c) is still 2 feet
* The initial velocity (v) is now 20 feet/second
* The target height (h) is still 20 feet
So the equation is:
20 = -16t^2 + 20t + 2
0 = -16t^2 + 20t + 18 (subtract 20 from both sides)
Evaluating the discriminant:
(20)^2 - 4(-16)(-18) = 400 - 288 = 112
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- 1. Converting Vertex Form to Standard Form Remember to FOIL
- 2. Vertex to Standard Form 1. Rewrite the binomial squared as a binomial times a binomial.
- 3. Vertex to Standard Form 2. Off to the side F.O.I.L the two binomials. 3. Combine like terms.
- 4. Vertex to Standard Form 4. Replace the two binomials with our new trinomial You must use Parenthesis!
- 5. Vertex to Standard Form 5. Distribute the monomial to the trinomial. 6. Combine like terms.
- 6. Additional Examples EX EX ANSWER ANSWER