Review for Quarter 3 Cumulative Test
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- Mervin McDowell
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1 Review for Quarter 3 Cumulative Test I. Solving quadratic equations (LT 4.2, 4.3, 4.4) Key Facts To factor a polynomial, first factor out any common factors, then use the box method to factor the quadratic. o When you have a nonmonic quadratic ax 2 + bx + c ( ), the numbers to fill in your box must multiply to a c and add to b To solve a quadratic equation, make sure one side of the equation is equal to 0. Then factor the quadratic and set all factors equal to 0. Solve all of the new equations for x. The quadratic formula gives the solutions to any quadratic ax 2 + bx + c = 0 o x = b ± b2 4ac 2a Practice Problems 1. Factor the following expressions. Don t forget to look for common factors first. (LT 4.2, 4.3) a. x! 3x 10 b. 2x! 14x! + 24x c. 4x! 8x 5 d. 3x! + 14x 5 1
2 2. Solve the following equations by factoring and using the zero product property. a. x! 4x 12 = 0 b. x! + 3x = 0 3. Solve the following equations using the quadratic formula. Give your answers with square roots and as decimals. a. x! + x 4 = 0 b. 2x! 5x + 1 = 0 c. 3x! x 3 = 0 d. x! 3x 3 = 0 2
3 II. Finding the vertex of a parabola (LT 4.5) Key Facts Quadratic graphs have a parabola shape or ( ) and are symmetric There are two ways to find the vertex (min or max point) of a quadratic: o Find the zeros (x-intercepts) by factoring or using the quadratic formula and average them to find the x-coordinate of the vertex o Use the formula x = b to find the x-coordinate of the vertex 2a Once you know the x-coordinate of the vertex, plug that back into the original quadratic formula to find the y-coordinate. Remember, the vertex is a point so your answer should be in the form (x, y) Practice Problems 4. Find the vertex of the following quadratic equations by solving and averaging the roots. a. x! + 12x + 32 = 0 b. 4x! + 15x 4 = 0 3
4 5. Find the vertex of the following quadratic equation by using the formula x =!!!!. Don t forget to find the y-value as well as the x-value. a. y = 2x! 8x + 1 b. y = x! + 3x 10 III. Projectile Motion (LT 4.1, 4.5) Key Facts Know how to use the formulas for projectile motion. The formulas will be given to you on the test, but you ll need to know what the variables stand for: Horizontal: x f = x i + v xi t Vertical: y f = y i + v yi t gt 2 v yf = v yi + gt Variable Meaning Variable Meaning x Initial horizontal i v Initial horizontal position = 0 m xi velocity x Final horizontal f v yi Initial vertical velocity position y Initial vertical Gravitational Constant = i g position 10 m s! y Final vertical f t Time position 4
5 Horizontal: x f = x i + v xi t Vertical: y f = y i + v yi t gt 2 v yf = v yi + gt Practice Problems 6. A projectile is shot into the air from a height of 5 meters. It is shot with an initial velocity of 30 m/s at an angle of 20. Variable Known? Variable Known? x i v xi x f v yi y i g y f t a. How far has the projectile traveled horizontally after 0.8 seconds? b. How much time has passed when the ball hits the ground? Use the quadratic formula to solve. c. What is the maximum height the projectile reaches? At what time does it reach that height? This means you must find the vertex of a quadratic. 5
6 Horizontal: x f = x i + v xi t Vertical: y f = y i + v yi t gt 2 v yf = v yi + gt 7. A projectile is shot into the air from a height of 1 meter. It is shot with an initial velocity of 10 m/s at an angle of 70. Variable Known? Variable Known? x i v xi x f v yi y i g y f t a. What is the maximum height the projectile reaches? At what time does it reach that height? b. What is the height of the projectile after 1.2 seconds? c. How long does it take for the projectile to hit the ground? 6
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Pre Chapter 9 Coverage Quadratic (2 nd Degree) Form a type of graph called a parabola Form of equation we'll be dealing with in this chapter: y = ax 2 + c Sign of a determines opens up or down "+" opens
Transformations with Quadratic Functions KEY
Algebra Unit: 05 Lesson: 0 TRY THIS! Use a calculator to generate a table of values for the function y = ( x 3) + 4 y = ( x 3) x + y 4 Next, simplify the function by squaring, distributing, and collecting
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Algebra Unit 4 Graphing Quadratics Name Quest Mission 1 Graph Quadratic Functions in Standard Form Objectives: Graph functions expressed symbolically by hand and show key features of the graph, including
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Math 2201 Unit 4: Quadratic Functions 16 Hours 6.1: Exploring Quadratic Relations Quadratic Relation: A relation that can be written in the standard form y = ax 2 + bx + c Ex: y = 4x 2 + 2x + 1 ax 2 is
But a vertex has two coordinates, an x and a y coordinate. So how would you find the corresponding y-value?
We will work with the vertex, orientation, and x- and y-intercepts of these functions. Intermediate algebra Class notes More Graphs of Quadratic Functions (section 11.6) In the previous section, we investigated
) 2 + (y 2. x 1. y c x2 = y
Graphing Parabola Parabolas A parabola is a set of points P whose distance from a fixed point, called the focus, is equal to the perpendicular distance from P to a line, called the directrix. Since this