Spring Showcase Project/Math/Quadratics

Vocab

100

What is the definition of a vertex?

The point of intersection of lines or the point opposite the base of a figure.

200

What is the definition of a parabola?

A parabola is a plane curve formed by the intersection of a right circular cone and a plane parallel to an element of the curve.

300

What is the axis of symmetry? 

A line that divides a figure in half so that each half is the mirror image of the other.

400

How is the quadratic equation written?

ax²+bx+c=0

500

 If I'm trying to find the zeros of a function, I'm looking for...

x-intercepts

Factoring Quadratics

100

Factor. x² − 7x − 18

(x − 9)(x + 2)

200

Factor. p²−5p−14

(p+2)(p−7)

300

Factor. 7k² + 9k

k(7k + 9)

400

Factor. 9r²−5r−10

Not factorable.

500

Factor. 28n⁴+ 16n³ − 80n²

4n²(7n − 10)(n + 2)

Solving Quadratics

100

Solve. (x−4)²−9=0

x=7 and x=1

200

Solve. x²+14x+45=0

x=−5 and x=−9

300

Solve. 4x²−100=0

x=5 and x=−5

400

Solve. 6x²−48x−54=0

x=9 and x=−1

500

Solve. x(x+4)=32

x=4 or x=-8

Squaring Quadratics

100

Solve the equation by completing the square. 

x²+6x-7=0

x=1 or x=-7

200

Solve the equation by completing the square.

2x²-10x-3=0

x=50

300

Solve the equation by completing the square.

-x²-6x+7=0

x=-1 or x=7

400

Solve the equation by completing the square.

3x²+10-25=0

x=5/3 or x=-5

500

Solve the equation by completing the square.

3x-121=0

It can't be solved by completing the square.

Random

100

If I'm trying to find the zeros of a function, I'm looking for...

x-intercepts

200

The y-value wher teh parabola intersectes the y-axis.

y-intercept

300

Solve using the quadratic formula.

b²−4b+4=0

{2}

400

Solve by completing the square.

x²+6x+8=0

{−2, −4}

500

Factor. 7x²−32x−60

(7x+10)(x−6)