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Chapter 5 Exam Review y = !2x + Consider the quadratic equation: 1.) The above equation is in ____________ form. 2.) Find the vertex. 2 x +1 3.) Find the x-intercepts of the equation by using the completing the square method. Simplify your answer. 4.) Find the discriminant. How many x-intercepts does this indicate ? 5.) Verify the above x-intercepts by using the quadratic formula. Simplify. 6.) Is the equation factorable ? If so, verify the x-intercepts by factoring to solve. 7.) Can you isolate x to solve ? If so, isolate x to solve. If not, explain why you cannot. 8.) Put the above equation in vertex form. Verify that the vertex is the same as in #2. 9.) Show how to find the EXACT x-intercepts from the vertex form of the equation in #8. 10.) Graph y = !2x 2 + x + 1 using the information from above AND by plotting two OTHER points on the graph. 11.) Use your graphing calculator to verify that you found the correct vertex and x-intercepts. Chapter 5 Exam Review Consider the quadratic equation: y = !3(x ! 2)2 + 5 1.) The above equation is in ____________ form. 2.) Find the vertex. 3.) Find the EXACT x-intercepts of the equation. 4.) Write the above equation in standard form. 5.) Find the discriminant. How many x-intercepts does this indicate ? 6.) Verify the above x-intercepts by using the quadratic formula. Simplify. 7.) Is the equation factorable ? If so, verify the x-intercepts by factoring to solve. 8.) Graph y = !3(x ! 2) + 5 using the information from above AND by plotting two OTHER points on the graph. 2 9.) Use your graphing calculator to verify that you found the correct vertex and x-intercepts. Chapter 5 Exam Review y = 2x ! 8 Consider the quadratic equation: 1.) The above equation is in ____________ form. 2.) Find the vertex. 2 3.) Find the discriminant. How many x-intercepts does this indicate ? 4.) Verify the above x-intercepts by using the quadratic formula. Simplify. 5.) Is the equation factorable ? If so, verify the x-intercepts by factoring to solve. 6.) Can you isolate x to solve ? If so, isolate x to solve. If not, explain why you cannot. 7.) Put the above equation in vertex form. Verify that the vertex is the same as in #2. 8.) Graph y = 2x 2 ! 8 using the information from above AND by plotting two OTHER points on the graph. 9.) Use your graphing calculator to verify that you found the correct vertex and x-intercepts. Chapter 5 Exam Review Graph the system of quadratic inequalities. y > !x 2 ! 4x y " x 2 + 7x + 10 Solve the quadratic inequalities. x 2 ! 7x < !4 !x 2 + x + 6 " 0 Write a quadratic function whose graph has the given characteristics. Vertex ( -3, 2) Vertex (4, 5) Point: ( -1, -18) Point: (8, -3) A baton twirler tosses a baton into the air. The path of the baton can be modeled by y = !16x 2 + 45x + 6 where y is the height of the baton from the ground (in ft) at a horizontal distance of x ft from the twirler. Find the horizontal distances of the baton from the twirler when it is 35 ft above the ground.