Linear Legends
Find the rate of change (slope) for the table where x increases by 1 and y increases by 15.
15 (the change in y over the change in x).
Factor the expression x^2-49.
(x - 7)(x + 7).
Simplify the radical v /-36 using the imaginary unit i.
6i
If f(x) = x^2 what is the equation of the graph shifted up 4 units?
f(x) = x^2 + 4
Evaluate the expression |2x - 10| when x = 3.
4 (since |2(3) - 10|=|- 4|= 4)
What is the y-intercept of the equation y = 4x - 12?
-12 (or the point (0, -12)).
Find the vertex of the function f(x) = (x - 5)^2+10.
(5, 10).
Solve the equation x^2 = -81 over the complex numbers.
x = +9i.
Describe the transformation of g(x) = (x + 7)^2 compared to the parent function.
Shifted left 7 units.
Simplify the radical /72 to its simplest radical form.
6/2
Write the equation in standard form for a line passing through (0, 0) with a slope of 5.
5x - y = 0 (Starting from y = 5x).
Solve x^2 - 10x + 25 = 0 by factoring.
x = 5 (Double root).
Multiply the binomials (3 + 2i) (3 - 2i).
13 (Using the pattern a^2 + b^2 for conjugates: 3^2 + 2^2).
Reflect the function y =( x - 2 )+ 5 across the y-axis.
y = |- x - 2|+ 5 (which simplifies to y = |x + 2| + 5).
Determine the average rate of change for f(x) = x^2 over the interval [1, 3].
4
Determine the solution to the system: {y = 3x, y = x + 4}.
(2, 6) (Substitute 3x for y: 3x = x + 4 → 2x = 4 → x = 2).
A ball is thrown into the air. If its height is h(t) = -16t^2+ 64t, at what time t does it hit the ground?
4 seconds (Set h (t) = 0 → -16t(t - 4) = 0).
Factor the sum of squares: 4x^2 + 25.
(2x + 5i) (2x - 5i).
Write the equation for a parabola with a vertex at (2, -3) that has been stretched vertically by a factor of 2
y = 2(x - 2)^2 - 3.
How many real solutions does a quadratic have if the discriminant (b^2 - 4ac) is equal to -15?
Zero (two imaginary solutions)
Identify the linear inequality represented by a dashed line through (0, -2) and (2, 0) shaded above the line.
y > x - 2 (The slope is 1, y-intercept is - 2, and it is shaded above).
Use the Quadratic Formula to find the roots of x^2— 5x - 1 = 0.
5+/2
X= —————-
2
Write the quotient 10/3-i in the form a + bi.
3 + i (Multiply top and bottom by 3 + i).
Identify the domain and range for the function f(x) = -/x + 2.
Domain: x ≥ 0; Range: y ≤ 2.
Use square roots to solve (x - 4)^2 = -12.
X=4+2i/3