Quarterly Review Geometry Academy Directions: Everyone is to record their answer on the dry erase board. You may work together with your group members.

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Presentation transcript:

Quarterly Review Geometry Academy

Directions: Everyone is to record their answer on the dry erase board. You may work together with your group members. I ENCOURAGE THIS! I will randomly pick a person from a group to answer the question to earn a point for your team. So, make sure that everyone agrees on the answer, because you never know who I am going to pick

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Writing Equations A plumber charges $50 plus $35 per hour. The cost to fix her plumbing will be $155. Write an equation to represent the situation. How many hours will the plumber work? (Solve the equation) h = 155 h = 3 The plumber will work 3 hours

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Solving Equations Solve the equation. SHOW ALL WORK! -3(2x + 5) = - 21 X = 1

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Solving Equations Solve the equation. SHOW ALL WORK! 7(8x – 11) – 9 = -422 X = - 6

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Shapes of Quadratics Write an equation that would be WIDER than y = 0.5x 2 Any “a” value that is SMALLER than 0.5 Example: y = 0.1x 2

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Shapes of Quadratics Write an equation that would be SKINNIER than y = 0.5x 2 Any “a” value that is BIGGER than 0.5 Example: y = 5x 2

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Quadratics on the Move Phil graphs the equation y = x What is the new equation if the graph is shifted down 8 units? y = x 2 - 3

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Writing Inequalities Write an inequality for each expression. Tyheim’s height is at least 6 feet X ≥ 6

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Writing Inequalities Write an inequality for each expression. I can spend at most $15 for dinner X ≤ 15

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Writing Inequalities Write a system of equations to represent the situation. Do not solve. The owner of a men’s clothing store bought 6 belts and 8 hats for $140. A week later, at the same prices, he bought 9 belts and 6 hats for $132. Find the price of a belt and the price of a hat. 6b + 8h = 140 9b + 6h = 132

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Quadratic Vertex What is the vertex of the parabola? Write the axis of symmetry equation. (-3, 4) X = - 3

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Verifying Solutions Verify if the point is on the graph of the equation 5x – 4y = 20. a.(6, 2.5) YES 5(6) – 4(2.5) = 20

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Verifying Solutions Verify if the point is on the graph of the equation 5x – 4y = 20. b. (2, -2) NO 5(2) – 4(-2) ≠ 20

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Verifying Solutions Verify if the point is on the graph of the equation 5x – 4y = 20. a.(6, 2.5) b. (2, -2) c. (1.6, -3) YES 5(6) – 4(2.5) = 20 NO 5(2) – 4(-2) ≠ 20 YES 5(1.6) – 4(-3) = 20

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Writing Inequalities Write an inequality statement that matches the number line graph. X ≥ 2

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Rewriting Equations a) Rewrite the equation into slope-intercept form. -2x -4y = 8 b) Identify the slope & y-intercept y = -2 – 1/2x m (slope) = -1/2 b (y-intercept) = -2

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Graphing Functions Graph the linear equation: -2x – 4y = 8

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Solving Systems of Equations Write a system of equations to represent the situation and solve the problem. SHOW WORK! On one day, 4 gardeners and 4 helpers earned $360. On another day, working the same number of hours and at the same rate of pay, 5 gardeners and 6 helpers earned $480. How much does a gardener and how much does a helper earn each day? 4g + 4h = 360 5g + 6h = 480 g = 60 h =30

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X & Y Intercepts a) Find the x-intercept from the graph. Write it as an ordered pair (x,y). b) Find the y-intercept from the graph. Write it as an ordered pair (x,y). (2, 0) (0, 4)

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Types of Solutions Draw a picture of a graph that has 1 solution. Draw a picture of a graph that has no solution. Draw a picture of a graph that has infinitely many solutions.

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Graphing Systems of Equations

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Graphing Inequalities Graph y ≥ -3x + 2 Step 1: Graph the line. m:________ b:________ Step 2: Dashed or solid line? Step 3: Shade above or below? -3/1 2

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Graphing Inequalities Graph 3x - 4y > 12 Step 1: Graph the line. m:________ b:________ Step 2: Dashed or solid line? Step 3: Shade above or below? 3/4 -3

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Graphing System of Inequalities Graph y ≤ 1/2x + 2 y < -2x - 3

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