| Factoring Quadratics | Graphing Quadratics | The Quadratic Formula | Double Trouble! |
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The root is = (-1,0).
(x+1)^2
What are the roots of x^2 + 2x + 1 = 0 ? This should be easy.
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X = -1.
(x+1)(x+1)
What are the roots of x^2 + 2x + 1 = 0 ? This should be easy.
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Two distinct real roots.
Using the discriminant, how many roots does x^2 - 7x + 4 = 0 have?
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x = (-1 +- root 57 ) /4
Use the Quadratic Formula to find the roots of
2x^2 = 7 - x |
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The roots are (0,0) and (5,0).
(x)(x-5)
What are the roots of k^2 - 5k = 0 ?
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It will be 84 units from the kicker when it lands.
A ball is kicked and can be modelled with the equation h(x) = -0.01x^2 + 0.84x
How far is the ball when it lands? |
M = (-0.3 +- root 0.17) / 0.4
-1.78 and 0.28
What are the exact roots of 0.2m^2 = -0.3m + 0.1 ?
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No solution.
Use the Quadratic Formula to find the roots of -4x^2 - 6x - 3
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(2y + 3x)(2y - 3x)
What is 4y^2 - 9x^2 = 0 factored?
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X = 3.5cm.
A rectangle has the dimensions of x + 10 and 2x - 3, where x is in centimetres. The area of the rectangle is 54cm^2. What is the value of x?
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The arch is 5 meters wide.
A mural has a parabolic arch in it. The arch can be modelled by the function h(d) = -0.4(d - 2.5)^2 + 2.5 where h is the height of the arch and d is the distance, both in meters. How wide is the base of the arch?
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x = (5 +- root 13) /2
Use the Quadratic Formula to find the roots of 1 + 3/x^2 = 5/x
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X is -7 and 3.
(x+7)(x-3)
What is y^2 + 4y = 21 ?
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She is 3.1 meters from the platform.
A diver jumps off of a 10-meter high diving board. Her height in meters above the surface of the water can be measured by the function h(d) = -2d^2 + 3d + 10 . How far is she from the platform when she enters the water?
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X = (1 +- root 19) / 3
What are the roots of x^2/2 - x/3 = 1 ?
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-x^2 + 3x + 5
What is the equation of (-3 +- root 29) /-2 ?
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20cm and 21cm.
The hypotenuse of a right triangle measures 29cm. One leg is 1cm shorter than the other. What are the the lengths of the legs?
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K = 9.
What does k have to be for x^2 + 6x + k = 0 and have one real root?
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B = 13, x = 3/2 .
One root of the equation 2x^2 + bx - 24 = 0 is -8. What are the possible values of b and the other root?
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1.5 meters.
A garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all around it, increasing the total area to 285 square meters. What will be the width of the pathway?
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