“The Graph Who Lived”
(Functions & Graphs)
(Functions & Graphs)
Harry graphs a line with slope 2 and y-intercept 3. What is the function?
f(x) = 2x + 3
Solve the system of equations by graphing:
y = \frac{1}{2}x - 2
y = 2x + 1.
The solution is (-2, -3).
Add:
(2x^2 - 5x + 2) + (3x^2 + 5x - 3)
5x^2 - 1
Factor completely:
100 - 49x^2
(10 - 7x)(10 + 7x)
Find the roots of the function f(x) = 9x^2 - 4.
x = \pm\frac{2}{3}
You plan to visit Disneyland and California Adventure. You want to spend more than 3 hours at Disney and at least 2 hours at California. However, you have no more than 7 hours total for both parks.
Write a system of inequalities that models this situation.
d + c \leq 7
d > 3
c \geq 2
If f(x) = x^2 - 4x + 3, find f(2).
f(2) = -1
Solve the system of equations by substitution:
y - 4x = - 7
x + y = -5
The solution is (2/5, -27/5).
Subtract:
(3x^2 - 4x) - (2x^2 + 2x + 2)
x^2 - 6x - 2
Factor completely:
45y^4 - 20y^2
5y^2(3y - 2)(3y + 2)
Solve the equation using the quadratic formula:
x^2 - 8x + 10 = 0
x = 4 \pm \sqrt{11}
Watermelon cost $0.25 each and apples cost $0.75 each. Write an inequality that represents the amount of watermelon and apples you can buy if you have at most $5 to spend.
.25w + .75a \leq 5
Identify the vertex and axis of symmetry for the function f(x) = -x^2 + 6x - 5.
The vertex is (3, 4), and the axis of symmetry is given by the equation x = 3.
Solve the system of equations by elimination:
4x - 3y = 1
12x - 15y = -3
The solution is (1, 1).
Multiply:
(x - 2)(2x - 7)
2x^2 - 11x + 14
Factor completely:
2x^2 − 4x + 2
(2x - 2)(x - 1)
Find the vertex, min/max, domain, and range for
f(x) = -4(x + 1)^2 + 5
Vertex: (-1, 5)
Max: 5
Domain: all real numbers
Range:
y \leq 5
A square courtyard (25 ft per side) is changed: shrunk by x on two sides, extended by x on the other two. Write a polynomial (in standard form) for the new area.
A = -x^2 + 625
Compare g(x) = -\frac{1}{2}x^2 to f(x) = x^2. How did f change to become g
Opens downward, vertically compressed.
At Honeydukes, Six chocolate frogs and two juices costs 22 dollars, while five chocolate frogs and three juices costs 21 dollars. Find the cost of each.
Chocolate Frog - 3.00
Juice - 2.00
Divide:
\frac{9b - 27}{-3}
-3(b - 3)
Factor completely:
x^3 + x + 2x^2 + 2
(x^2 + 1)(x + 2)
Complete the square:
x^2 + 22x + 25 = 0
(x + 11)^2 = 96
The height of a falling broomstick is modeled by the function h(t) = -16t^2 + 32. When does it hit the ground?
t = \sqrt{2}