Find the zeros of each parabola. a) y =x2 +2x - 3 I need help with this ASAP

1. What value of k makes each quadratic expression a perfect square trinomial? a) x2-10x+k b) x2+3x+k
2. Find the vertex of the following quadratics by completing the squares
c) y=2x2-18x-18 c) y=2x2-14x-16
f) y=2(x-1)2-8
4. A ball is kicked into the air and follows a path described by h = -4.9t2 +6t +0.6where t is the time in seconds and is the height in metres.
a) How high is the ball off the ground when it is kicked?
b) What is the height of the ball after 1second?
c) What is the maximum height of the ball, to the nearest tenth of a metre?
d) When does the ball reach the maximum height?
e) When does the ball return to its initial height, rounding to two decimal places?
5. The length of a rectangle is 1 m more than the width. If the area of the rectangle is 20 metres square, what are the dimensions of the rectangle?
6. a)=ax2+bx+c withrootsof6and-7.
b) What would happen to the roots if you multiplied both sides of the equations in
part a) by 3? Explain.
7. Given the parabola y = 2x2 + 4x - 6, find:
a) The equation of the parabola infactored form.
b) The equation of the parabola invertex form.
c) What are the x-intercepts?
8. Find the equation of the parabola in vertex form that has x-intercepts of -1and 3, that passes through the point (5, 6).
9. A parabola has vertex (-3,7), and one x-intercept is -11. Find the other x-intercept and the y-intercept.
a) y=x2+10x+6 b) y=-3x2+6x+l
3. Find the zeros of each parabola. a) y =x2 +2x - 3
b) y=4x2-36
d) y=16x2+40x+25 e) y=3x2+28x+9
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10. A path of a toy rocket is defined by the relation y=-3x2 +11x+ 4, where x is the horizontal distance (in metres), above the ground.
a) Determine the zeros of the relation.
b) For what values of x is the relation valid?
c) How far has the rocket travelled horizontally when it lands on the ground? d) What is the maximum height of the rocket above the ground?
11. For each quadratic relation, use the discriminant to determine how many roots there are for each.
a) 2x2+9x–3=0
b) -3x2–8x+2=0
c) x2–4x+5=0
d) x2-12x+36=0
12. The cost, in dollars, of operating a machine per day is given by the formula
C = 3t2 – 96t + 1014, where t is the time the machine operates, in hours.
a) What is the minimum cost of running the machine?
b) For how many hours must the machine run to reach this minimum cost?
13. The three sides of a right triangle are consecutive even integers. What is the length of each side?
14. A rectangle has dimensions 3x +1 and 2x – 5. Its area is 1,150 cm2. What are its dimensions?
15. If two different quadratic relations have the same zeros, will they necessarily have the same axis of symmetry? Will they have the same vertex? Explain your reasoning.
Answers
1. 52, (3/2)2
2. Vertex: (-5, -19). (1, 4), (4.5, -58.5),
3. a.-3,-1 b.-3,3 c.8,-1 d.-5/4 e.-1/3,-9 f.-1,3
4. 0.6m, 1.7m, 2.4, 3/4.9 sec, 1.2 sec
5. 4and5

6. x=6,x=7
7. x=-1,x=3
8. a=1⁄2,(h, k)=(1,-2)
9. x= -11, x = 5, y-int (0, 4.75)
10.a. -1/3, 4 b. any real numbers c. 4.3m d. 11.1 m 11. 2 roots, 2 roots, no root, one root
12.16 hrs, cost $246
13. 6, 8, 10
14. 25, 46