3.1 Quadratic Functions and Inequalities

Question 1

a function defined by a one or more monomials

Answer 1

polynomial function

Question 2

a function that is a second-degree polynomial

Answer 2

quadratic function

Question 3

vertex form of a quadratic formula

Answer 3

Question 4

general form of a quadratic function

Answer 4

Question 5

What should you do to rewrite a quadratic function into vertex form?

Answer 5

Complete the square on ONLY one side of the function.

Question 6

How do you determine the direction of the opening of a quadratic function?

Answer 6

See if the “a” value is > or < than 0. If a > 0, the parabola opens up. If the a < 0, the parabola opens down.

Question 7

What is the equation of a vertex of a parabola in general form?

Answer 7

Question 8

What is the equation of the axis of symmetry of a parabola in general form?

Answer 8

Question 9

A minimum or maximum value in a quadratic function must happen at the _______?

Answer 9

Vertex. The minimum or maximum value is the “y” coordinate of the vertex

Question 10

What are the parts to a parabola?

Answer 10

1) vertex
2) focus
3) Latus Rectum
4) Directrix
5) Axis of symmetry

Question 11

Draw the parts of a parabola.

Answer 11

Question 12

When asked to identify the characteristics of a graph, what items should be included in your answer?

Answer 12

1) Vertex
2) Direction of Opening
3) Axis of Symmetry
4) Domain
5) Range
6) Location of maximum or minimum (x - value)
7) Maximum or minimum (y-value)
8) intervals of increase or decrease
9) X-intercepts
10) y-intercepts

Question 13

How do you find the x-intercepts of a quadratic equation

Answer 13

1) Factor
2) Square root principle
3) Completing the square
4) Quadratic formula

Question 14

How do you find the y-intercept of a quadratic equation.

Answer 14

1) Plug in 0 for x and solve for y. (0,y)
or
2) If the equation is in general form the y-intercept is always the “C” value (0, c)

Question 15

How do you solve quadratic inequalities using a graph?

Answer 15

1. Get 0 on one side of the inequality and a quadratic polynomial on the other side
2. Final all roots to the corresponding quadratic equation.
3. Graph the corresponding quadratic function. The roots from (2) determine the x-intercepts (make sure to identify if open or closed circle).
4. If > look for the intervals above the x-axis.
5. If < look for intervals below the x-axis.
6. Write answer in interval notation.