Problem Solving Involving Quadratic Equation

Question 1

What is the general form of a quadratic equation?

Answer 1

ax^2 + bx + c = 0

Question 2

What is the quadratic formula used for?

Answer 2

To find the solutions (roots) of a quadratic equation

Question 3

True or False: A quadratic equation always has two solutions.

Answer 3

True

Question 4

What is the discriminant of a quadratic equation?

Answer 4

b^2 - 4ac

Question 5

When the discriminant is greater than zero, how many real solutions does a quadratic equation have?

Answer 5

Two distinct real solutions

Question 6

Fill in the blank: If the discriminant is equal to zero, the quadratic equation has ________ real solution(s).

Answer 6

One

Question 7

What is the vertex form of a quadratic equation?

Answer 7

y = a(x-h)^2 + k

Question 8

What does the ‘a’ value in a quadratic equation determine?

Answer 8

The direction and width of the parabola

Question 9

What does the ‘h’ value in the vertex form of a quadratic equation represent?

Answer 9

The x-coordinate of the vertex

Question 10

What does the ‘k’ value in the vertex form of a quadratic equation represent?

Answer 10

The y-coordinate of the vertex

Question 11

What is the axis of symmetry of a quadratic function?

Answer 11

x = h

Question 12

What does the axis of symmetry of a quadratic function represent?

Answer 12

The line that divides the parabola into two symmetrical halves

Question 13

Fill in the blank: The vertex of a parabola is the ________ point on the graph.

Answer 13

Minimum or maximum

Question 14

What is the standard form of a quadratic function?

Answer 14

y = ax^2 + bx + c

Question 15

What is the relationship between the roots and the coefficients of a quadratic equation?

Answer 15

The sum of the roots is -b/a and the product of the roots is c/a

Question 16

What does the term ‘quadratic’ mean in a quadratic equation?

Answer 16

Involving the square of a variable

Question 17

What is the maximum number of real solutions a quadratic equation can have?

Answer 17

Two

Question 18

What is the process of completing the square used for in solving quadratic equations?

Answer 18

To convert a quadratic equation into vertex form

Question 19

What is the ‘y-intercept’ of a quadratic function?

Answer 19

The point where the graph intersects the y-axis

Question 20

What is the ‘x-intercept’ of a quadratic function?

Answer 20

The point(s) where the graph intersects the x-axis

Question 21

What is the ‘domain’ of a quadratic function?

Answer 21

All real numbers

Question 22

What is the ‘range’ of a quadratic function?

Answer 22

Depends on the value of ‘a’, typically y >= k for a > 0 and y <= k for a < 0

Question 23

What is the ‘vertex’ of a quadratic function?

Answer 23

The highest or lowest point on the parabola

Question 24

What is the ‘minimum’ of a quadratic function?

Answer 24

The lowest point on the parabola

Question 25

What is the ‘maximum’ of a quadratic function?

Answer 25

The highest point on the parabola

Question 26

What is the ‘root’ of a quadratic equation?

Answer 26

The solution(s) to the equation that make it true

Question 27

What is the ‘discriminant test’ used for in quadratic equations?

Answer 27

To determine the number and nature of the roots of a quadratic equation

Question 28

What is the ‘quadratic function’ of a quadratic equation?

Answer 28

A function of the form f(x) = ax^2 + bx + c

Question 29

What is the ‘parabola’ of a quadratic equation?

Answer 29

The U-shaped graph of a quadratic function