Quadratic Functions
What is the location of the vertex of the quadratic function?
y = 2(x - 3)2 + 5
The point (3, 5).
What are the solution to the equation:
|x| = 5
x = 5 and x = -5.
Copying these three parts of a triangle results in a new triangle that is similar to the original triangle, but might not be congruent. What are they? (Do not give only letters!)
Angle-Angle-Angle
What is the expression you would use to find the x-value of the midpoint between (-3, 5) and (7, -13). Do not simplify, just give the numerical expression?
x = (7 + (-3))/2
**This would result in x = 2.**
What is the sport that Mrs. Tabola's youngest son plays?
Baseball
The direction the graph of a quadratic function opens is based on what value? Be specific and give examples.
The value of 'a', or the coefficient of x2 .
For example, y = 2x2 is a quadratic function that opens UP. And y = -2x2 opens DOWN.
What are the solutions to the equation:
|x - 3| + 12 = 7
NO SOLUTION
What is the congruence theorem that is specific to only right triangles? (Do not give only letters!)
Hypotenuse-Leg
What is the expression I would use to find the distance between (-5, 5) and (1, 13)?
Do not simplify, just give the numerical expression.
D = sqrt[ (1 - (-5))2 + (13 - 5)2 ]?
**This distance would be D = 10.**
How many grandkids does Mrs. Tabola have?
1 grandson
When factoring the quadratic expression:
3x2 + 13x - 10
what are the terms that go on the TOP of the X-Game and the BOTTOM of the X-Game. (Be specific.)
The TOP is 3x2*-10 = -30x2.
The BOTTOM is 13x.
What are the values of the f(x) when x = -2, 1, and 4.
f(x) = { -3x + 2, x < 1
{ 5x, x >= 1
f(-2) = 8
f(1) = 5
f(4) = 20
What are four congruence theorems that can be used to prove that two triangles are congruent? (Do not give only letters!)
Side-Side-Side
Side-Angle-Side
Angle-Side-Angle
Angle-Angle-Side
FREE POINTS!!
Your team gets 300 free points.
Where is Mrs. Tabola right now (the town)?
Castle Rock, CO
What is the formula used to solve quadratic equations? (This is not the NAME, it is the actual formula.)
x = [-b +- sqrt(b2 - 4ac) ]/ (2a)
Write this function as a piecewise function:
f(x) = 3|x + 1| - 5
f(x) = { -3(x + 1) - 5, x <= -1
{ 3(x + 1) - 5, x > -1
What is the combination of parts of a triangle that does NOT prove congruence? (Do not give only letters!)
Side-Side-Angle?
(Or Angle-Side-Side)
I know that the midpoint of the segment between A and B is (-1, 4).
What is the equation you would use to find 'y' if A = (-3, 10) and F = (x, y)?
Do not simplify, just give the equation.
(10 + y)/2 = 4?
**This value would be y = -2.**
Where does Mrs. Tabola spend her winters?
Scottsdale, AZ
What is the final SIMPLIFIED answers when you solve a quadratic equation and get:
x = -3 +- sqrt(-50)
x = -3 + 5sqrt(2)i
and
x = -3 - 5sqrt(2)i
What are the steps you would go through to find the inverse of the function f(x) = 3(x - 2) + 5? Be specific and through.
1. Swap x and y to get x = 3(y - 2) + 5.
2. Solve for y to get y = (x - 5)/3 + 2.
3. Write this in correct notation: f-1(x) = (x - 5)/3 + 2
What are the only two tools that can be used in geometric constructions?
A compass and a straight edge
What is the distance rounded to the nearest tenth between the points (-2, 5) and (5, -7)?
D = 13.9
How many and what "kinds" of kids does Mrs. Tabola have?
TWO step-daughters and TWO sons
BONUS if you also stated that she has ONE son-in-law.