MCAP Jeopardy (APEX Version)

Quadratic Functions

100

Factor the quadratic 4x³-6x²-28x

2x(2x-7)(x+2)

200

Solve the equation x²+8x=20

x=2 and x=-10

300

Find the x-intercepts and the vertex of y=(x-4)(x+2)

x-intercepts: (4,0) and (-2,0)

vertex: (1, 9)

400

Solve the system of equations

4x-8y=0

x²+y²=25

x=2sqrt(5)=4.472

x=-2sqrt(5)=-4.472

y=sqrt(5)=2.236

y=-sqrt(5)=-2.236

500

Jose needs to enclose a rectangular section of his yard.  The perimeter of the section is 27 feet, and the area is 35 square feet.  Find the length and width.

Length = 10 feet

Width = 3.5 feet

Transforming Functions

100

Given G(x)=(x+3)/2 and f(x)=2x-3, are the functions inverses?

Yes

200

Compare G(x)=5(x-3)²+2 to the parent function, what transformations are present?

Vertical Stretch by a factor of 5, shifted right 3, shifted up 2

300

Given f(x)=-5(x-3)³+4, compared to the parent function, what transformations are present?

Reflected over the x-axis, vertical stretch by a factor of 5, shifted right 3, shifted up 4

400

Write the equation for the quadratic, if the vertex is (-1,-4) and the y-intercept is (0,8).

y=12(x+1)^2-4

500

Give the quadratic equation that would be flipped over the x-axis, stretched vertically by a factor of 3, shifted down 4 units, and shifted left 1 unit.

y=-3(x+1)^2-4

Polynomials Functions

100

Simplify the expression given below:

(3x-4x²+8x³)-(-6x+2x⁴-5x²)

-2x^4+8x^3+x^2+9x

200

Simplify the expression given below:

(3x³-2x²+7)(x³+2x)

3x^6-2x^5+6x^4+3x^3+14x

300

Divide the polynomials given below:

(2x²-4x+2)/(x-1)

2x-2

400

Is (x-2) a factor of F(x)=x⁴-2x³+3x²-10x+3?

No

500

Find the roots of the polynomial function given below:

g(x)=x³-7x²-x+7

x=1, x=-1, x=7

Rational Expressions and Functions

100

Determine what values of x make the expression undefined.

(x+1)/(x²+2x-24)

x=-6 and x=4

200

Simplify the expression given below:

3/(x^2-25)-1/(x+5)

(-x+8)/((x+5)(x-5))

300

A model airplane will be an exact copy of the original, but at 1/50 the size.  The original airplane is 230 feet long.  How long should the model be?

4.6 feet

400

Simplify the expression given below:

(x^2+5x+6)/x^2/(x^2-3x-10)/x^2

(x+3)/(x-5

500

Identify the y-intercept, holes/asymptotes, and domain.

(x^2-5x+6)/(x^2-x-2)=g(x)

y-intercept: (0,-3)

Hole: x=2

Asymptote: x=-1

Domain: (-inf, -1)U(-1,2)U(2,inf)

Radical Expressions and Functions

100

Solve the equation:

sqrt(3x+54)+6=10

x=-38/3

200

Solve the equation:

sqrt(17-x)=x+3

x=1

Extraneous Solution: x=-8

300

Simplify the expression given below:

(3+i)(-4+3i)

-15+5i

400

Simplify the expression given below:

(5+2i)+(8-3i)

13-i

500

Solve the equation given below:

sqrt(9x+378)=3sqrt(7x)

x=7