Quadratic Functions Theory (Studies)

Question 1

What is a quadratic?

Answer 1

The general quadratic looks like:

ax² + bx + c

“Quad” means “square”, which in math means to the power of 2. So a quadratic is an equation that contains an x², and this is the highest power. There can’t be, for example x³, nor x⁴, and so on. Only the square is the highest power. Quadratic expression contains three terms, which makes it a trinomial.

Question 2

What is a constant?

Answer 2

A constant is a number that is not attached to a variable (like an x, or any other number).

e.g. 3x² + 4x + 7

7 is the constant.

3 and 4 are coefficients.

3 is the leading coefficient.

Question 3

What is a coefficient?

Answer 3

A coefficient is a number that is multiplying (it is attached to) a variable, like an x or any other letter.

e.g.

3x² + 2x - 4

3 is the coefficient of x²,

and 2 is the coefficient of x.

Question 4

What is the leading coefficient?

Answer 4

The leading coefficient, is the number that is attached to the x with the highest power.

e.g. in the trinomial

4x² + 3x + 9

the leading coefficinent is 4

Question 5

How can you recognize that an equation is quadratic?

Answer 5

Some variable is squared.

It can always be written as:

ax²+bx+c=0

Question 6

What are the three ways to solve a quadratic equation?

Answer 6

• Factorization
• Completing the square
• The quadratic formula

Question 7

What does the graph of f(x)=x² look like? What are the vertex and line of symmetry?

Answer 7

Vertex: (0,0)

Line of symmetry: x=0

Question 8

How do you find the x-intercept of ANY function?

Answer 8

You plug in 0 for y and solve for x….because when you’re on the x-axis, the y-coordinate MUST be equal to 0.

Question 9

How do you find the y-intercept of ANY function?

Answer 9

You plug in 0 for x and solve for y….because when you’re on the y-axis, the x-coordinate MUST be equal to 0.