Equations and Inequalities
Solve for m.
-2.5m - 52 = 4.6m + 19
m = -10
A line passes through (3, 4) and (-1, -1). Write the function in slope-intercept form.
y = (5/4)x + (1/4)
In the function f(x) = 3(4)x, what do the 3 and 4 represent?
The 3 is the initial value (y-intercept) of the function. It is the y-value of the function when x = 0.
The 4 is the constant ratio of the function. It is the number you multiply by to get from one y-value to the next.
Find the vertex of the function f(x) = 2x2 - 4x + 10.
(1, 8)
Factor the polynomial.
x2 - 14x - 51
(x - 17)(x + 3)
Solve for x.
-3x - 8 < -4x + 1
x < 9
A line passes through (0, 2) and (-1, 9). Write the function in point-slope form.
OR
y - 9 = -7(x + 1)
Does the function g(x) = 0.75(3x) represent exponential growth or exponential decay?
Exponential growth.
Find the axis of symmetry of the function q(x) = 5x2 - 9.
x = 0
The function f(x) = (x + 4)2 - 3 is the quadratic parent function translated ___ units (left/right) and ___ units (up/down).
4 units left, 3 units down
Solve for k.
|k + 4| - 5 = 10
k = 11, k = -19
Write the equation of a line that is parallel to y = -3x + 10 and passes through the point (0, 3).
y = -3x + 3
What are the domain and range of the function h(x) = -4(2)x?
Domain: All real numbers
Range: y < 0
Which value of a would make the graph of h(x) = ax2 open downward and be wider than the graph of the quadratic parent function?
A) -3
B) 5/2
C) -0.5
D) 1/4
C, -0.5
Simplify the radical expression.
√72 + √98 = ?
13√2
Solve the system of equations.
y = 3x - 5
6x - 3y = 9
(2, 1)
Write the equation of the line that is perpendicular to y = -4x + 9 and passes through the point (8, -5).
y = (1/4)x - 7
Write the exponential function that passes through the given points.
(0, 4)
(1, 4/3)
(2, 4/9)
(3, 4/27)
f(x) = 4(1/3)x
Write the quadratic function in standard form that passes through the point (0, 4) and has a vertex at (-1, 3).
f(x) = x2 + 2x + 4
What kind of function does the list of ordered pairs show? Why?
(-1, 4) (0, 6) (1, 12) (2, 22) (3, 36)
Solve the system of inequalities (you will need paper for this).
8x + 4y > 24
y > 2x - 10
idk look at the graph.
Jerome is selling cakes today. He sells cakes for $10 each. He sold 5 cakes yesterday. Write a function that models the overall amount of money, y, that he makes after selling x cakes.
y = 10x + 50
Maria buys a car for $15,000. The value of the car depreciates 5.4% annually. Write a function to model the value of Maria's car after x years.
f(x) = 15,000(0.946)x
OR
f(x) = 15,000(1 - 0.054)x
Find the x-intercept(s) of the function h(x) = -3x2 + 7x - 13.
There are no x-intercepts.
A rectangle has an area of 2x2 - 3x - 30 square feet. What are the length and width of the rectangle?
(2x + 5) feet and (x - 4) feet.