Let’s Review the Quadratic Formula & Completing the Square!!

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Presentation transcript:

Let’s Review the Quadratic Formula & Completing the Square!!

You must have a QUADRATIC before solving! Quadratic Formula You must have a QUADRATIC before solving!

Quadratic Formula: Make sure each variable is in parenthesis. Solve for the discriminant. JUST the part UNDER the radical. Split up the fractions. Simplify each fraction.

Example A:

Completing the Square: Put in standard form. Move “c” to the other side. Add to both sides of the equation . Write as a Take the square root of both sides Simplify

Example B:

You Try! 1) 2)

What about…

IRRATIONAL How do I find the x-intercepts of a polynomial equation that will not factor?

IRRATIONAL ROOTS This will occur when you get a polynomial after synthetic division that CANNOT be factored! But you MUST get it down to a quadratic! Might need to use the Quadratic Formula:

f(x) = x4 + 3x3 – 5x2 – 15x 1 3 -5 -15 -3 x = 0 , -3 1 3 -5 -15 -3 15 What if it doesn’t factor to begin with or you aren’t sure? Find a root to begin synthetic division using your calculator, and get it down to a quadratic! f(x) = x4 + 3x3 – 5x2 – 15x x = 0 , -3 1 3 -5 -15 -3 1 3 -5 -15 -3 15 1 -5

Find all of the roots of: g(x) = x4 + 2x3 – 5x2 – 4x + 6 (-3 and 1 using the calculator) Find all of the roots of: g(x) = x4 + 2x3 – 5x2 – 4x + 6 ANSWER: -3, 1, ,

Find all of the roots of: g(x) = 4x3 – 16x2 + 11x + 3 (x=3 using the calculator) Find all of the roots of: g(x) = 4x3 – 16x2 + 11x + 3 ANSWER: 3, ,

Find all of the zeros of: g(x) = 3x3 – 22x2 + 32x + 32 (x=4 using the calculator) Find all of the zeros of: g(x) = 3x3 – 22x2 + 32x + 32 ANSWER: 4, 4 ,

Find all of the roots of: g(x) = x3 – x2 – 11x + 3 (x=-3 using the calculator) Find all of the roots of: g(x) = x3 – x2 – 11x + 3 ANSWER: -3, ,

Work and sketch on a separate piece of paper. Homework!! Work and sketch on a separate piece of paper.