Quadratic Equations
A solution to the quadratic equation y = 5x2 + wx - 6 is the point (1, 3). Solve for w.
w = 4
Is the point (2, -5) a solution to the inequality y > 3x2 - 4x - 7 ?
No
Find the values for a and b such that the sum of a + 3i and 12 - bi is 15 + i.
a = 3
b = 2
Solve: x(x - 4) = -5
x = 2 + i
x = 2 - i
Solve: x2 < 2x + 3
Put your answer in interval notation.
(-1, 3)
Find the product of 4 + 2i and 10 - 5i.
50
Solve: x2 - 6x = -4
x = 3 + V5
x = 3 - V5
*V is "square root"*
Solve. Express your answer in interval notation.
4x2 + 3x > 2x2 + 5
(-infinity, -2.5) U (1, infinity)
Write y = x2 + 12x + 32 in vertex form.
y = (x + 6)2 - 4
Determine the value of a such that y = ax2 + 4x + 2 will have one real solution.
a = 2
Graph the quadratic inequality y > 2x2 - 12x + 10. You may NOT use a calculator.
See doc.
*DOUBLE JEOPARDY*
Solve the system graphically. You may NOT use a calculator.
y < 0.5x + 4
y ≥ x2
See doc.
Solve the system algebraically.
y = -x2 - x + 12
y = x2 + 7x + 12
(0, 12) and (-4, 0)
Write the quadratic inequality for the parabola shown (see doc) in standard form.
y > x2 + 3x - 4
An airline transports 800 people a week between two cities. A round trip ticket cost $300. The company wants to increase the price. They estimate that for each $5 increase 10 passengers will be lost. What ticket price will maximize their income?
$350 per ticket