Factoring
Factor fully:
2x2 + 8x
2x(x+4)
What is the optimal value? Will it be a maximum or minimum?
f(x) = -4(x+5)2 + 7
Max is 7
Express as a mixed radical in simplest form.
√392
14√2
Find the roots of the following quadratic equation:
0 = x2 - 2x - 15
x = -3 and x = 5
Find the family equation for a quadratic function with zeros of 24 and -42.
f(x) = a(x - 24)(x + 42)
Factor fully:
x2 + 5x + 6
(x+2)(x+3)
Find the optimal value of:
f(t) = -5t2 + 40t + 100
Then state whether it is a max or min.
The maximum value is 180
Simplify the following radical:
√44 + √88 + √99 + √198
5√11 + 5√22
Determine the value for k for which the quadratic equation has one root
0 = 9x2 +kx + 25
k = 30
Find the specific family member of a quadratic function that has zeros of 5 + √7 and 5 - √7 and passes through the point (2 , 15)
f(x) = 15/2(x - 5 - √7)(x - 5 + √7)
Factor fully:
9 - 4k2
-(2k - 3)(2k + 3)
Determine the min or max coordinates of the following quadratic function by completing the square:
f(x) = x2 - 6x + 8
Vertex: (3, -1)
Minimum value = -1
Multiply and then simplify your answer:
√70 ⋅ √26
2√455
Find the exact roots of:
0 = 9x2 + 4x - 16
x = (-2 ± 2√37)/9
Determine algebraically whether the linear and quadratic functions intersect and if they do intersect how many points of intersection there will be for the following system:
Line: y = 3x + 5
Quadratic: f(x) = 3x2 - 2x -4
D = 133
D > 0 so there are two solutions meaning two points of intersection exist in this system of equations.
Factor fully:
4m2n - 28mn2 + 49n3
n(2m - 7n)2
Last year, the Musical tickets were sold for $11 each and 400 people attend. It have been determined that an increase of $1 in ticket price would cause a decrease in attendance of 20 people. What ticket price would maximize revenue?
$15.50
Give the simplest form of the product of:
(3√5 + √6)(√5 - 2√6)
3 - 5√30
The power consumption of a school cafeteria is approximated by P(x) = -0.25x2 + 6x + 14, where x is the number of hours after 12:00 AM and P is the power consumption in kW.
Determine how long the power consumption is at least 40 kW.
12.65 hours
Determine the exact value of the x-values of the points of intersection between:
Line: 4x - y = 5
Quadratic: f(x) = 6x2 - 7x - 15
(-2/3,-23/3)
(5/2,5)
Factor fully:
x2 - y2 - 2yz - z2
(x + y + z)(x - y - z)
Randy is building a fence at the side of his warehouse. He has 120m of fencing to work with and is using the side of the warehouse as one side of the rectangular fenced area. What are the dimensions of the maximum area that Randy can enclose?
30m by 60m
Rationalize:
4 / (5 - √3)
(10 + 2√3)/11
Given the quadratic 0 = x2 + kx + 4, determine the restrictions on k so the equation has two distinct real roots.
k < -4 and k > 4
Write the simplified standard form for the quadratic with:
- x-intercepts at 2 ± √5
- Pass through (5,4)
f(x) = x2 - 4x - 1