Name: Date: Period: A2H.L5-7.WU Quick Review SOLVING QUADRATICS Find the roots of the equation using two methods. 2x 2 + 4x 6 = 0
Algebra Objective Language Objective A2H.L5-7.NOTES LESSON 5-7: USING QUADRATIC FORMULA Students will be able to use the quadratic formula to find the solutions of a quadratic function. Students will use the value of the discriminant to make predictions about the graph of a quadratic function and determine the number of solutions of the related quadratic equation. Vocabulary A. The are the point(s) where the graph crosses the x-axis and the y-value is. These points are also called,, or. B. You can find the x-intercepts by solving a quadratic equation. The quadratic formula is especially important when the equation cannot be. You can use it as an alternative method to completing the square. C. The quadratic formula will give real number roots, real number double root, or real number roots ( roots). x = b ± b2 4aa 2a D. The value of the, b 2 4aa, can be used to predict the number of real roots.
SOLVING USING THE QUADRATIC FORMULA Solve each equation below by using the quadratic formula. A2H.L5-7.NOTES Example #1: Standard form? 2x 2 + 4x 6 = 0 Example #2: x 2 + 6x = 7 Standard form? a = b = c = a = b = c = Replace a, b, and a in the formula. x = b ± b2 4ac 2a Replace a, b, and a in the formula. x = b ± b2 4ac 2a x = ± x = ± Simplify using PEMDAS. Start w/the x = ± x = ± Simplify using PEMDAS. Start w/the x = ± x = ± x = ±
Investigating the Discriminant: SECTION 1/PART A y = x 2 x 6 PART B Solve using the quadratic formula. x 2 x 6 = 0 PART C Value of the Discriminant Identify the a, b, and a and calculate the Give the value of the discriminant and state whether it is positive, negative, or zero. y = x 2 x 6 a = b = a = How many x-intercepts do you see? How many solutions are there? The value of the discriminant is: What are the x-intercepts? (Write them as ordered pairs!) The solutions are: Is it positive/negative/zero?
SECTION 2/PART A y = x 2 + 10x + 25 PART B Solve using the quadratic formula and by factoring. x 2 + 10x + 25 = 0 PART C Value of the Discriminant Identify the a, b, and a and calculate the Give the value of the discriminant and state whether it is positive, negative, or zero. y = x 2 + 10x + 25 a = b = a = How many x-intercepts do you see? How many solutions are there? The value of the discriminant is: What are the x-intercepts? (Write them as ordered pairs!) The solutions are: Is it positive/negative/zero?
SECTION 3/PART A y = x 2 4x + 8 PART B Solve using the quadratic formula and completing by the square. x 2 4x + 8 = 0 PART C Value of the Discriminant Identify the a, b, and a and calculate the Give the value of the discriminant and state whether it is positive, negative, or zero. y = x 2 4x + 8 a = b = a = How many x-intercepts do you see? How many solutions are there? The value of the discriminant is: What are the x-intercepts? (Write them as ordered pairs!) The solutions are: Is it positive/negative/zero?
SECTION 4: Summarize Answer the questions below. Look back at the previous pages if you need help! Consider y = x 2 x 6 (Section 1) Consider y = x 2 + 10x + 25 (Section 2) Consider y = x 2 4x + 8 (Section 3) When the discriminant was positive/negative/zero there were 0/1/2 solutions and 0/1/2 x-intercept(s). When the discriminant was positive/negative/zero there were 0/1/2 solutions and 0/1/2 x-intercept(s). When the discriminant was positive/negative/zero there were 0/1/2 solutions and 0/1/2 x-intercept(s). 1. How does finding the value of the discriminant help us to determine the number of solutions to a quadratic equation? Use the discriminant to answer the questions below. Keep in mind that x-intercepts are also called solutions, roots and zeros. 2. Determine the nature and the number of solutions for the quadratic equation x 2 + 12x + 11 = 0. 3. How many x-intercepts does the graph of y = x 2 + 6x + 9. 4. Use the discriminant to verify that there are no real number solutions for the quadratic equation shown below. If you were to graph this function, how many x-intercepts would there be? Why? What do we call this type of root? 3x 2 + 5x + 3 = 0 If you were to graph this function, how many x-intercepts would there be? Why? 5. REASONING For what values of k does the equation x 2 + kx + 9 = 0 have one real solution? two real solutions? 6. ERROR ANALYSIS If one quadratic equation has a positive discriminant, and another quadratic equation has a discriminant equal to 0, can the two share a solution? Explain why or why not. Suppose one equation is x 2 + 8x + 16. Create a second quadratic equation that would meet the given criterion.
Name: Solve the equation using the Quadratic Formula. 1. 2x 2 + 8x = 6 A2H.L5-7 Lesson Check: PRECISION Find the discriminant of each quadratic equation. Determine the number of real solutions. 2. x 2 + 2x 9 = 0