4.2 – Quadratic Equations. “I can use the discriminant to describe the roots of quadratic equations.” DISCRIMINANT: b 2 – 4ac b 2 – 4ac > 0 2 distinct.

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Presentation transcript:

4.2 – Quadratic Equations

“I can use the discriminant to describe the roots of quadratic equations.” DISCRIMINANT: b 2 – 4ac b 2 – 4ac > 0 2 distinct real roots b 2 – 4ac = 0 Exactly one real root (called a double root) b 2 – 4ac < 0 No real roots (2 distinct imaginary roots)

Conjugates A pair of complex numbers in the form a + bi and a – bi. Imaginary roots of polynomial equations with real coefficients always occur in conjugate pairs.

“I can solve a quadratic equation by graphing, factoring, and using the Quadratic Formula.” Method Situation Graphing Best to use when approximating and verifying solutions. If the discriminant < 0, there will be no x-intercepts Factoring Best to use when a, b, and c are integers and the discriminant = 0 or a perfect square. It cannot be used when the discriminant < 0. Quadratic FormulaThis will work for any quadratic equation.

Use the equation: x 2 + 2x – 8 = 0 First, approximate the zeros by graphing. Looks to be at x = -4 Looks to be at x = 2

Use the equation: x 2 + 2x – 8 = 0 Next, solve by factoring: x 2 + 2x – 8 = 0 (x – 2)(x + 4) = 0 (x – 2) = 0 and (x + 4) = 0 x = 2 and x = -4

Use the equation: x 2 + 2x – 8 = 0 Last, use the Quadratic Formula to solve: x = -2 + √ 2 2 – 4(1)(-8) 2(1) x = -2 + √ 36 2 x = x = -2 – x = 2 and x = -4

Solve 2t 2 + 5t + 4 = 0

10 ft x x x 15 ft x Write a quadratic equation to model this situation: The area of a garden is to be a third of the total area. There is a walkway around it of uniform width, and the dimension of the entire area is 15 feet by 10 feet.

Homework 4.2 p219 # 28 – 32, 36 Extra Credit (5 points) must be completed on your own # 38