Converting between forms.
Standard/Factored/Vertex
Standard/Factored/Vertex
The same quadratic is listed in three different forms. Determine which is in standard, factored, and vertex form.
f(x) = (x + 3)2 - 4
g(x) = x2 + 6x + 5
h(x) = (x + 5)(x + 1)
Vertex Form: f(x) = (x + 3)2 - 4
Standard Form: g(x) = x2 + 6x + 5
Factored Form: h(x) = (x + 5)(x + 1)
Which is the graph of f(x) = -(x + 3)2
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The Green Graph
Solve the quadratic for ANY/ALL solutions by factoring:
x2 - 7x - 18 = 0
x = -2, 9
Using the variables a, b, and c in a quadratic written in standard form, ax2 + bx + c = 0, what would have to be added to both sides of the equation to complete the square?
(b/2)2
The value of half of b, squared.Determine the values of a, b, and c in the following quadratic equation.
-x2 - 6x + 16 = 0
Bonus 200 points if you can solve it!
a = -1
b = -6
c = 18
Bonus: x = -8, 2
Rewrite the quadratic in standard form:
f(x) = (x + 5)2 - 10
f(x) = x2 + 10x + 15
Match each function to its graph:
f(x) = x2
g(x) = (x - 5)2 + 4
h(x) = (x + 5)2 - 4
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(Green): f(x) = x2
(Blue): g(x) = (x - 5)2 + 4
(Red): h(x) = (x + 5)2 - 4
Solve the quadratic for ANY/ALL solutions by factoring:
x2 - 36 = 0
x = -6, 6
If using the method of completing the square to solve the quadratic equation x2 + 16x - 5 = 0, which number would have to be added to "complete the square"?
64
Write the quadratic formula.
Bonus 200 points if you sing the song!
x = (-b ± √ (b2 - 4ac)) / 2a
Rewrite the quadratic in standard form:
f(x) = (x - 2)(x + 5)
f(x) = x2 + 3x - 10
In proper interval notation, determine the Domain and Range of the graph of the function f(x) = -(x - 3)2 + 4
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Domain: (-∞, ∞) "all real numbers"
Range: (-∞, 4]
Solve the quadratic for ANY/ALL solutions by factoring:
x(x - 7) = 0
x = 0, 7
Solve using square roots:
x2 - 144 = 0
x = -12, 12
Use the quadratic formula to solve the equation for any/all real solutions. Show all work and round your answer to the nearest hundredth if necessary.
2x2 - 4x - 15 = 0
Quadratic Formula: x = (-b ± √ (b2 - 4ac)) / 2a
x = -3/2 (or -1.5) and 5
Rewrite the quadratic in standard form:
f(x) = -(x + 3)2 + 12
f(x) = -x2 - 6x +3
Determine the following key features of the graph of the function f(x) = x2 + 2x - 8
Axis of Symmetry Equation
Vertex Coordinate
X-Intercept Coordinates:
Y-Intercept Coordinate:
Another Point on the Graph:
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Axis of Symmetry Equation: x=-1
Vertex Coordinate: (-1, -9)
X-Intercept Coordinates: (-4, 0) and (2, 0)
Y-Intercept Coordinate: (0, -8)
Another Point on the Graph: (-2, -8) (1, -5) (-3, -5)
Solve the quadratic for ANY/ALL solutions by factoring:
x2 - 2x = 35
x = -5, 7
Solve using square roots:
x2 + 25 = 0
No solution!
Use the quadratic formula to solve the equation for any/all real solutions. Show all work and round your answer to the nearest hundredth if necessary.
x2 - 5x + 9 = 0
Quadratic Formula: x = (-b ± √ (b2 - 4ac)) / 2a
No Solutions.
You cannot take the square root of a negative number.
Rewrite the quadratic in vertex form. (Hint: complete the square)
f(x) = x2 + 4x - 5
f(x) = (x + 2)2 - 9
Graph f(x) = -(x + 3)2 + 4 and include the following key features:
Vertex, X-Coordinates, Y-Coordinate and its reflection point.
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Vertex: (-3, 4)
X-Coordinate: (-5, 0) and (-1, 0)
Y-Coordinate: (0, -5)
Y-Coordinate Reflection Point: (-6, -5)
Solve the quadratic for ANY/ALL solutions by factoring:
x2 -7x - 7 = 2x + 3
x = -1, 10
Solve by completing the square. Show all steps.
x2 + 4x = 5
x = -5, 1
Use the quadratic formula to solve the equation for any/all real solutions. Show all work and round your answer to the nearest hundredth if necessary.
x2 - 7x - 25 = 0
x = -2.60, 9.60