Quadratics

Quadratic Formula

Discriminant

Solve the Quadratic Equation using ______.

Solve

Functions and graphs

100

What is the quadratic formula?

x=(-b+-sqrt(b^2-4ac))/(2a)

100

If the discriminant is 15, how many solutions and what type are they?

2 real solutons

100

Write the coefficients of the equation (when in standard form):

11x^2-5x=-2

a=11, b=-5, c=2

100

x^2+8x+12=0

x=-4, -6

100

Write the general form for a quadratic in standard form.

ax^2+bx+c=0

200

What does the quadratic formula find?

The zeros or x-intercepts

200

If the discriminant is -900, how many solutions are there?

2 imaginary solutions.

200

Solve using factoring.

2x²-18x + 40 = 0

x = 4

x = 5

200

x²+ 4x = 0

x = 0, -4

200

What is the vertex of y = 2x² - 5

(0, -5)

300

Using the quadratic formula find the zeros:

y = x²- 5x + 6

x = 3

x = 2

300

What is the discriminant of the following equations:

y=x²+4x+6

discriminant = -8

300

Solve using factoring.

0 = x²- 8x +16

x = -4

300

5x²+1=126

-5

300

Find the vertex of f(x) = x² + 2x +1

vertex (-1 0)

400

Solve the equation using the quadratic formula:

0 = x²+ 9x + 20

x = -5

x = -4

400

What is the discriminant of the following equations:

y=2x²+3x-10

400

Solve using the quadratic formula.

x² + 6x + 2 = 0

x = 3 - sqrt(7) ,3+sqrt(7)

400

3x² + 5x = 2x

x = 0, -1

400

What is the maximum or minimum value of

f(x) = 5 - 4x - x²

The maximum value is 9

500

Solve using the quadratic formula:

0 = x²+ 7x + 20

(-7+-sqrt(31)i)/2

500

What does the discriminant tell you?

The number and type of solutions that a quadratic has.

500

Solve using whatever method you think is most appropriate.

3x²- 4x + 4 = 0

𝑥 = 2/3 ± (2√2𝑖)/3

500

Solve: x²+ 25 = 0

x= 5i , -5i

500

Where is the axis of symmetry of a function that has a y-intercept in -12 and zeros in -2 and 6?

x = 2