5.3 Solving Quadratic Equations by Finding Square Roots.

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Presentation transcript:

5.3 Solving Quadratic Equations by Finding Square Roots

EXAMPLE 1 Use properties of square roots Simplify the expression. 5= 4a = = 3 14b = 9 14 = c = 4 = 2929 d = 7 =

_____________ 2._____________ ____________ 2.____________ _____________ 2._____________ _____________ 2._____________ _____________ 10._____________ _____________ 10._____________ Show all work! Simplify each of the following. Leave each answer in radical form.

GUIDED PRACTICE for Example ANSWER ANSWER

GUIDED PRACTICE for Example ANSWER ANSWER

EXAMPLE 2 Rationalize denominators of fractions. Simplify (a) 5 2 and SOLUTION (a) = = 5 2 = (b) SOLUTION (b) = – 2 2 = 21 – – = 21 –

EXAMPLE 3 Solve a quadratic equation Solve 3x = 41. 3x = 41 Write original equation. 3x 2 = 36 Subtract 5 from each side. x 2 = 12 Divide each side by 3. x = + 12 Take square roots of each side. x = Product property Simplify

EXAMPLE 3 Solve a quadratic equation ANSWER The solutions are and – Check the solutions by substituting them into the original equation. 3x = 41 3( ) = ? 41 = 41  3(12) + 5 = 41 ? 3x = 41 3( ) = 41 – 23 ? 41 = 41  3(12) + 5 = 41 ?

EXAMPLE 4 Standardized Test Practice SOLUTION 1515 (z + 3) 2 = 7 Write original equation. (z + 3) 2 = 35 Multiply each side by 5. z + 3 = + 35 Take square roots of each side. z = – Subtract 3 from each side. The solutions are –3 + and –3 – 35 ANSWER The correct answer is C.

GUIDED PRACTICE for Examples 2, 3, and 4 GUIDED PRACTICE Simplify the expression ANSWER – 21 – – 6 7 – 5 8 – ANSWER

– for Examples 2, 3, and 4 GUIDED PRACTICE 15. – – 3 ANSWER

for Examples 2, 3, and 4 GUIDED PRACTICE 17. Solve the equation. 5x 2 = z 2 – 7 = (x – 2) 2 = ANSWER

EXAMPLE 5 Model a dropped object with a quadratic function Science Competition For a science competition, students must design a container that prevents an egg from breaking when dropped from a height of 50 feet. How long does the container take to hit the ground ? SOLUTION h = – 16t 2 + h 0 Write height function. 0 = – 16t Substitute 0 for h and 50 for h 0. – 50 = – 16t 2 Subtract 50 from each side = t 2 Divide each side by – = t Take square roots of each side t Use a calculator. ANSWER Reject the negative solution, –1.8, because time must be positive. The container will fall for about 1.8 seconds before it hits the ground.

Homework: Simplifying radicals worksheet and Pg. 267 #47-67o, 69, 70