Unit 5 Quadratic Relations Review PDF

**[Unit 5 Quadratic Relations Review]** 1. Graph the following relations on the grid by filling out the corresponding table of values. X Y ---- --- -3 -2 -1 0 1 2 3 a. [*y* = *x*^2^ − 2*x*]{.math.inline} b. [*y* =  − *x*^...

**[Unit 5 Quadratic Relations Review]** 1. Graph the following relations on the grid by filling out the corresponding table of values. X Y ---- --- -3 -2 -1 0 1 2 3 a. [*y* = *x*^2^ − 2*x*]{.math.inline} b. [*y* =  − *x*^2^ + 4]{.math.inline} X Y ---- --- -3 -2 -1 0 1 2 3 2. Identify the vertex, axis of symmetry, zeros, the y-intercept and the max/min value of the quadratic relations in the question of above. a. Vertex b. Vertex ---- ------------------ -- ---- ------------------ -- Axis of Symmetry Axis of Symmetry Zeros Zeros y-int y-int Min/Max Min/Max 3. Determine whether each relation is linear or quadratic. Explain your reasoning. c. y = x +4 b. y = - x^2^ + 4x -- 3 c. y = ½ x + 2 d. y = 6 -- x + x^2^ e. y = 0 4. Determine whether each relation is linear, quadratic, or neither. (Show your calculations.) d. ----- ----- ------------------------- -------------------------- *x* *y* ***First Differences*** ***Second Differences*** -6 9 -5 4 -4 1 -3 0 -2 1 -1 4 0 9 ----- ----- ------------------------- -------------------------- ----- ----- ------------------------- -------------------------- *x* *y* ***First Differences*** ***Second Differences*** 1 4 2 8 3 12 4 16 5 20 6 24 ----- ----- ------------------------- -------------------------- e. ----- ----- ------------------------- -------------------------- *x* *y* ***First Differences*** ***Second Differences*** 1 5 2 6 3 5 4 2 5 -3 6 -8 ----- ----- ------------------------- -------------------------- f. 5. For the following parabolas, state the key features: a. a. Vertex a) Vertex b. Min/max value b) Min/max value c. Axis of symmetry c) Axis of symmetry d. Zeros d) Zeros e. y-intercept f) y-intercept 6. Find the **zeros** of the following quadratic equations without graphing. a. y = (x + 2)(x -- 4) d) y = 3x^2^ -- 48 b. y = x(x -- 8) e) y = x^2^ -- 81 c. y = x^2^ -- 8x -- 33 7. y = x^2^ + 6x + 9 g. Does the relation have a maximum or minimum value? h. What is the y-intercept? i. What are the zeros for the relation? 8. Cameron throws a football down a field. Its height is given by the equation h = -0.01(d-30)^2^ + 9. Where h is the height in metres of the ball and d is the distance the football has travelled down the field in metres. j. State the maximum height of the football. k. State the distance that the ball has travelled when it reaches it maximum height. l. State the football's height when it has travelled 25 metres down the field. m. How far has the football travelled when its height is 6 metres and it is going down. n. A receiver is standing 50 metres down the field. How high will he need to reach in order to catch the ball? 9. An arch for a bridge has the shape of a parabola according to the quadratic function y = -0.002x^2^ + 10. Where y is the arch's height in metres and x is the distance in metres a. State the height of the arch. b. State the length of the arch. c. What is the height of the arch 10 metres from an end? d. How high is the arch 10 metres from the centre of the arch? 10. Dylan fires a flare at a 70° angle and it flies according to the function h = -9(t-3)^2^ + 83, where H is the flare's height (metres) and t is the time (seconds) since the flare was fired. o. What was the flare's height when it was fired? p. What is the flare's height after 4 seconds? 11. Emma dives off a cliff into the water below. Her path can be modelled by the relation h = -4.9t^2^ + 4.9t + 21.5, where h is her height above the water in meters and t is the time in seconds. q. What is the height of the cliff? r. What height above the water is Emma after 1.5 s? 12. The path of a ball after it is kicked can be modelled by the equation [*h* =  − 5*t*^2^ + 25*t*]{.math.inline}, where [*h*]{.math.inline} is the height in meters and [*t*]{.math.inline} is the time in seconds. s. How long was the ball in the air? t. How long did it take the ball to reach its maximum height? u. What was the maximum height of the ball?