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Quadratic Formula
Quadratics cont.
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100
Factor the trinomial n^2 + 11n +24
Factors are (n + 8) (n + 3)
100
2. Factor out the GCF of the following expression 9xy^2 - 6x^2y
GCF is 3xy.
100
19. Use the quadratic formul to solve x^2 - 9x +20 = 0
x = 4, x = 5
100
9. Tell whether the function is quadratic. Explain. x -4 -2 0 2 4 y 10 -4 -6 4 26
Quadratic, 2nd difference is -12
100
What is the quadratic parent function?
y = x^2
200
Factor out the GCF of the following expression: 4y^2 + 6z^3 - 8
The GCF is 2.
200
4. Factor 3x^2 + 7x + 4
The factors are (3x +4)(x + 1)
200
20. Use the quadratic formula to solve -4x^2 - 24x - 36 = 0
x = -3
200
10. Sketch the graph of the quadratic function y = (1/2)x^2
parent vertically compressed by (1/2)
200
What is the general form for a quadratic equation?
ax^2 + bx + c
300
8. Factor x^2 - 25
Factors are (x - 5)(x + 5)
300
7. Factor 4x^2 + 12x + 9
Factors are (2x + 3)(2x + 3) or (2x + 3)^2
300
15. Use the quadratic formula to solve x^2 + 9x = 36
x = -12, x = 3
300
12. Find the domain and range of the given function.
D: {all real numbers} R: { y <= 5}
300
What is the quadratic formula?
-b +- square root b^2 - 4ac all divided by 2a
400
5. Determine whether 25w^6 - 81d^2 is a difference of two squares. If so, factor it. If not, explain why.
It is a difference of squares. (5w^3 - 9d)(5w^3 + 9d)
400
Factor 4x^2 - 25
Factors are (2x + 5) (2x - 5)
400
16. Use the quadratic formula to solve x^2 -7x = 44
x = -4, x = 11
400
11. Identify the vertex of the parabola. Then give the minimum or maximum value of the function.
The vertex is (1, -7) The minimum is -7.
400
14. A golfer hits the golf ball. The quadratic function y = -16x^2 + 48x gives the time x seconds when the golf ball is at height 0 feet. How long does it take for the golf ball to return to the ground?
3 seconds
500
4. Factor 3x^2 + 10x - 8
Factors are (x + 4)(3x - 2)
500
Factor 2x^2+3x -5
Factors are (2x + 5) (x - 1)
500
17. Use the quadratic formula to solve 4x^2 + 20x = -25
x = - 2.5
500
13. The trajectory of a model rocket launched from a rocket launcher on the ground at an angle of 65 degrees with an initial speed of 50 meters per second can be modeled by the parabola: 2.14x – 0.011x^2, where the x-axis is the ground. Find the height of the highest point of the trajectory and the horizontal distance the model rocket travels before hitting the ground.
Maximum (highest point) 104.08 or 104 meters Horizontal distance 194.5 meters
500
A golfer hits the golf ball. The quadratic function y = -16x^2 +48x gives the time x seconds when the golf ball is at height 0 feet. When does the golf ball reach its maximum height and what is the maximum height?
At 1.5 seconds and 36 meters