Solving Quadratic Equations II

Features of Parabolas

100

Identify a, b, and c:

x^2+6x+5=0

What is

a = 1, b = 6, c = 5 ?

200

Identify a, b, and c:

 -x² - 9x +20 = 0

What is

a = —1, b = -9, c = 20 ?

300

The following quadratic opens this direction

Y=2x^2-5x-3

What is

upward ?

400

The following quadratic has a maximum or minimum

 x² - 6x - 27 = 0

What is

a minimum?

500

A quadratic equation that has a discriminant of 0 has this many solutions

What is

one?

Quadratic Facts

100

When solving quadratic equations, we are trying to find what feature of the parabola?

What is the 

x-intercepts ?

200

What are the three different types of solutions we can have when solving quadratics

What is 

No solution, One solution or Two solutions ?

300

How do we know a quadratic function does not have solutions when looking at a graph?

What is

The parabola does not touch the x-axis (no x-intercepts) ?

400

Why is the quadratic formula useful for solving quadratic equations?

What is

We can ALWAYS use the quadratic formula, but we cannot always factor ?

500

How do we know a quadratic function does not have solutions when using the quadratic formula?

What is

There will be a negative number under the square root (The discriminant will be negative) ?

Features of Parabolas II

100

This is the point where a quadratic function crosses the y-axis

What is the 

y-intercept ?

200

This point is the center of a parabola and can be a maximum or minimum, depending on the direction of the parabola.

What is 

Vertex ?

300

This line passes through the vertex of a parabola and divides the parabola in half.

What is 

Axis of Symmetry ?

400

The x-coordinate of the vertex

What is 

the Axis of Symmetry?

500

Draw a sketch of a parabola and label the following features:

y-intercept, x-intercepts, vertex, minimum, axis of symmetry

Answers will vary.

Formulas

100

Standard form quadratic equation

What is

Y=ax^2+bx+c

200

Axis of Symmetry formula

What is

X=(-b)/(2a)

300

Discriminant formula

What is

b²-4ac ?

400

Quadratic formula

What is

(-b+-sqrtb^2-4ac)/(2a)

500

The Axis of Symmetry of this quadratic equation

2x^2-5x-3=0

What is

x = 5/4 or 1.25 ?

Solutions

100

Solve for the Axis of Symmetry for the following quadratic equation

x² - 11x + 24 = 0

What is

x = 11/2 Or 5.5 ?

200

Solve for the discriminant for the following quadratic equation

0 = x² +3x + 2

What is

1 ?

300

Solve: 

x² + 6x + 9 = 0

What is

x = -3 ?

400

Solve 

0 = x² +2x - 48

What is

x = -8 ,  x = 6 ?

500

Solve the following: 

2x² +18x + 39 = 0

What is

x = -3.64

x = -5.37 ?