9.1 Solving Quadratic Equations by Finding Square Roots Objectives 1. Evaluate and approximate square roots.

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1 9.1 Solving Quadratic Equations by Finding Square Roots 1. Evaluate and approximate square roots. 2. Solve a quadratic equation by finding square roots. Key Terms Square Root Radicand Perfect Squares Irrational Number Quadratic Equation Leading Coefficient Finding Square Roots. Find all square roots of the number or write no square roots

2 Evaluating Square Roots Evaluate the expression. Give the exact value if possible. Otherwise, approximate to the nearest hundredth. Evaluating Expressions Evaluate for the given values, if Evaluating Expressions Use a calculator to evaluate the expression. Round the result to the nearest hundredth. Solve the equation or write no solution. Falling Object Model Niagara Falls in New York is 167 feet high. How long does it take the water to fall from the top to the bottom of Niagara Falls? h = final height in feet. t = time in seconds s= starting height in feet.

3 9.2 Simplifying Radicals 1. Use properties of radicals to simplify radicals. Key Terms Simplest form (radicals)- Properties of Radicals Product Property- The square root of a product equals the product of the square roots of the factors. Example: Quotient Property- The square root of a quotient equals the quotient of the square roots of the numerator and denominator. Example: Simplify the expression

4 9.3 Graphing Quadratic Functions 1. Sketch the graph of a quadratic function. 2. Use quadratic models in real-life settings. Key Terms Quadratic Function- Standard Form- Parabola- Vertex- Axis of Symmetry- Graph of a Quadratic Function Graphing a Quadratic Function. The graph of If If is a parabola. is positive, the parabola opens up. is negative, the parabola opens down. The vertex has an x-coordinate of. The axis of symmetry is the vertical line. 1. Find the x-coordinate of the vertex. 2. Make a table of values, using x-values to the right and left of the vertex. 3. Plot points and connect them with a smooth curve to form a parabola.

5 Graphing a Quadratic Function with a Positive a- value. Sketch the graph of. 1. Find the vertex. 2. Make a table of values. x y 3. Plot the points from step 2.

6 Graphing a Quadratic Function with a Negative a- value. Sketch the graph of. 1. Find the vertex. 2. Make a table of values. x y 3. Plot the points from step 2. Using a Quadratic Model The path of the women s record breaking shot put throw can be modeled by where x is the horizontal distance in feet and y is the height in feet. 1. What is the maximum height in feet of the shot put?

7 9.4 Solving Quadratic Equations by Graphing 1. Solve a quadratic equation by graphing. Key Terms Roots- Use the graph to identify the roots of the equation. Use the graph to identify the roots of the equation.

8 9.5 Solving Quadratic Equations by the Quadratic Formula 1. Use the quadratic formula to solve a quadratic equation. 2. Use quadratic models for real-life situations. Quadratic Formula The quadratic formula is used to find the solutions (x-intercepts) of the quadratic equation when. Using the Quadratic Formula. Solve. Writing in Standard Form. Solve.

9 Finding the x- Intercepts of a Graph. Find the x-intercepts of the graph of. Vertical Motion Models. 9.1 Object is Dropped: Object is Thrown: ( ) ( ) ( ) ( ) You are competing in a field target event. You throw a marker down from an altitude of 200 ft. toward a target. When the marker leaves your hand, its speed is 30 ft. per second. How long will it take the marker to hit the ground?

10 9.6 Applications of the Discriminant 1. Use the discriminant to find the number of solutions of a quadratic equation. 2. Use the discriminant to solve real-life problems. Key Terms Discriminant- tells how many solutions a quadratic equation has. The Number of Solutions of a Quadratic Equation. Consider the quadratic equation. If is positive, then the equation has two solutions. If If is zero, then the equation has one solution. is negative, then the equation has no solution. Tell whether the equation has two solutions, one solution, or no real solution Find values of so that the equation will have two solutions, one solution, and no real solution.

11 You attach a stick to a rope and your friend is preparing to throw it over a tree branch that is 20 ft. from the ground. 1. Your friend can throw the stick upward with an initial velocity of 29 ft. per second from an initial height of 6 ft. Will the stick reach the branch when it is thrown? 2. You can throw the stick upward with an initial velocity of 32 ft. per second from the same initial height as your friend. Will the stick reach the branch when it is thrown?

12 9.7 Graphing Quadratic Inequalities 1. Sketch the graph of a quadratic inequality. Sketching the Graph of a Quadratic Inequality. 1. Sketch the graph of the equation that corresponds to the inequality. Sketch a dashed parabola for inequalities with < or > to show that the points on the parabola are not solutions. Sketch a solid parabola for inequalities with or to show that the points on the parabola are solutions. 2. The parabola you drew separates the coordinate plane into two regions. Test a point that is not on the parabola to find whether it is a solution of the inequality. 3. If the test point is a solution, shade its region. If not, shade the other region. Graphing a Quadratic Inequality. Sketch the graph of x y

13 Sketch the graph of x y

14 9.8 Comparing Linear, Exponential, and Quadratic Models 1. Choose a model that best fits a collection of data. Three Basic Models

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