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Unit 1 Test Review Graphing Quadratics

Question #1a Evaluate the expression for the following values of a and b: **Don’t forget to simplify. a = - 4, b = 8

Question #1b Evaluate the expression for the following values of a and b: **Don’t forget to simplify. a = -7, b = 112

Question #2a Write the coordinates of the vertex in the graph. Is the vertex a minimum or maximum?

Question #2b Write the coordinates of the vertex in the graph. Is the vertex a minimum or maximum?

Question #3 Graph f(x) = 2x2 + 4x – 1 What is the range? y ≥ -3 OR (-3,∞) y x

Question #3 Identify the characteristics of f(x) = 2x2 + 4x - 1 Vertex: __________________ Axis of Symmetry: _________________ Zero(s): _________________________ Domain: _________________________ Range: __________________________ Interval of Increase: ________________ Interval of Decrease: _______________ Rate of Change on -3 ≤ x ≤ -2: _________ Vertex: (-1, -3) Axis of Symmetry: x = -1 Zero(s): -2.25 and .25 Domain: (-∞, ∞) Range: [-3, ∞) Interval of Increase: (-1, ∞) Interval of Decrease: (-∞, -1) Rate of Change on -3 ≤ x ≤ -2: -6

Question #4 Axis of Symmetry: x = 2 Vertex: ( 2, 2) Find the axis of symmetry and vertex of y = 2x2 – 8x + 10: Axis of Symmetry: x = 2 Vertex: ( 2, 2)

Question #5 Firework displays are made up of “stars” that are ignited and projected into the air. Suppose a “star” is projected at a starting height of 480 ft with a velocity of 72 ft/s. The equation h(t) = -16t2 + 72t + 480 gives the star’s height h in feet at time t in seconds. a) Find the vertex. b) What is the maximum height of the star?

Question #5 Firework displays are made up of “stars” that are ignited and projected into the air. Suppose a “star” is projected at a starting height of 480 ft with a velocity of 72 ft/s. The equation h(t) = -16t2 + 72t + 480 gives the star’s height h in feet at time t in seconds. a) Vertex: (2.25, 561) b) 561 feet

Question #6 Over what interval is the graph increasing and decreasing? Increase: (1, ∞) Decrease: (-∞, 1) * Remember, always use the X value of your vertex

Question # 7 How many real roots does each graph have? 2 The parabola crosses the x axis twice The parabola does not cross the x-axis 1 The parabola touches once

Question #8 What is the range of the graph below? y ≥ -4 OR (-4, ∞)

Question #9 What is the domain of the graph? (-∞,∞)

Question #10 Which of the following means the same as “all real numbers less than or equal to -9” (9, ∞) (∞, -9) (9, -∞) (-∞, -9] D

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