Rules
What is always the domain in quadratic functions?
All Real Numbers
What is the formula for axis of symmetry? (aos)
x= -b/2a
Describe how "f(x)=(x+3)2-5" transforms.
Horizontal shift to the left by 3
Vertical shift down by 5
What does the "c" represent in the standard form of a quadratic function?
y-value in y-intercept
What is the vertex when the parabola is facing down
The vertex is the highest point aka the maximum.
What is the vertex form of the quadratic equation?
f(x) = a(x − h)2 + k, where a ≠ 0
Describe how "f(x)=4(x-2)2+2 transforms.
Stretches by the factor of 4
Horizontal shift to the right by 2
Vertical shift up by 2
What do the "h" and "k" represent in the function?
The "h" represents the horizontal shift while the "k" represents the vertical shift.
What is the vertex when the parabola is facing upwards?
The vertex is the lowest point aka minimum.
What is the formula for standard form?
f(x)=ax2+bx+c (a,b, and c are real numbers and a≠0)
Describe how "f(x) = -2(x+8)2+3" transforms.
Vertical shift up 3
Horizontal shift to the left 8
Reflect over the x-axis
Stretch by the factor of 2
How does the "a" impact the parabola?
If a is positive, the graph opens upward, and if a is negative, then it opens downward.
What is always the exponent used?
2
What is the parent function?
The parent function is y=x2.
Describe how "f(x)=7x2+13" transforms.
Stretches by a factor of 7
Vertical shift up by 13
What is the input variable?
The input variable is "x".
What are the directions a parabola can open in?
Upwards and Downwards
What is the unknown variable in the standard formula? What are the known variables in the standard formula?
The unknown variable is "x". The known variables are "a", "b", "c".
Describe how "f(x)=2x2" transforms.
Stretches by a factor of 2
What is the output variable?
The output variable is "y".