Order the group of quadratic functions from widest to narrowest graph.
yequals3xsquared, yequalsone third
xsquared, yequalsnegative 6xsquared
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Part 1
Choose the correct answer below.
A.
yequalsone third
xsquared, yequals3xsquared, yequalsnegative 6xsquared
B.
yequalsnegative 6xsquared, yequals3xsquared, yequalsone third
xsquared
C.
yequalsnegative 6xsquared, yequalsone third
xsquared, yequals3xsquared
D.
yequals3xsquared, yequalsone third
xsquared, yequalsnegative 6xsquared
E.
yequals3xsquared, yequalsnegative 6xsquared, yequalsone third
xsquared
F.
yequalsone third
xsquared, yequalsnegative 6xsquared, yequals3xsquared
The correct order from widest to narrowest graph is:
E. y equals 3x^2, y equals -6x^2, y equals one third x^2
Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the following function.
y equals x squared minus 8 x minus 9
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Part 1
What is the equation of the axis of symmetry?
enter your response here (Type an equation. Simplify your answer.)
Part 2
The vertex is
enter your response here. (Type an ordered pair.)
Part 1: To find the equation of the axis of symmetry, you can use the formula x = -b/(2a) where the equation is in the form y = ax^2 + bx + c.
In this case, the equation is y = x^2 - 8x - 9.
a = 1, b = -8, c = -9.
Therefore, x = -(-8)/(2*1) = 4.
So, the equation of the axis of symmetry is x = 4.
Part 2: To find the vertex, substitute x = 4 back into the original equation to find the y-coordinate.
y = (4)^2 - 8(4) - 9
y = 16 - 32 - 9
y = -25
Therefore, the vertex is at (4, -25).
Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the following function.
yequalsnegative 3 x squared plus 2 x minus 4
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Part 1
The axis of symmetry is xequals
enter your response here. (Simplify your answer.)
Part 2
The vertex is
enter your response here.
(Type an ordered pair. Simplify your answer.)
Part 1: To find the equation of the axis of symmetry, you can use the formula x = -b/(2a) where the equation is in the form y = ax^2 + bx + c.
In this case, the equation is y = -3x^2 + 2x - 4.
a = -3, b = 2, c = -4.
Therefore, x = -2/(2*(-3)) = -2/(-6) = 1/3.
So, the equation of the axis of symmetry is x = 1/3.
Part 2: To find the vertex, substitute x = 1/3 back into the original equation to find the y-coordinate.
y = -3(1/3)^2 + 2(1/3) - 4
y = -3(1/9) + 2/3 - 4
y = -1/3 + 2/3 - 4
y = -3/3 = -1
Therefore, the vertex is at (1/3, -1).
Solve the equation by finding square roots.
xsquaredminus121equals0
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Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A.
xequals
enter your response here (Simplify your answer. Use a comma to separate answers as needed.)
B.
The solution is not a real number.
To solve the equation x^2 - 121 = 0 by finding square roots:
1. Add 121 to both sides to isolate x^2:
x^2 = 121
2. Take the square root of both sides:
x = ±√121
x = ±11
Therefore, the solutions are:
A. x = 11, -11.
Write the following equation in standard form. Then solve.
4 q squared minus 4 qequals3 q squared minus 9 q plus 14
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Part 1
The equation in standard form is
enter your response here.
Part 2
qequals
enter your response here (Use a comma to separate answers as needed.)
To write the equation in standard form, we need to simplify it first:
Given equation: 4q^2 - 4q = 3q^2 - 9q + 14
Rearranging the terms:
4q^2 - 4q - 3q^2 + 9q = 14
Combining like terms:
q^2 + 5q - 14 = 0
Now, in standard form, the equation is:
q^2 + 5q - 14 = 0
To solve the equation, we can factor it:
(q + 7)(q - 2) = 0
Setting each factor to zero gives:
q + 7 = 0 --> q = -7
q - 2 = 0 --> q = 2
Therefore:
Part 1: The equation in standard form is q^2 + 5q - 14 = 0
Part 2: q = -7, 2