Quadratic Functions Theory (Studies) Flashcards Preview

VIS (2019): IB Math Studies > Quadratic Functions Theory (Studies) > Flashcards

Flashcards in Quadratic Functions Theory (Studies) Deck (9)
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1

 

What is a quadratic?

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

2

 

What is a constant?

 

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.

3

 

What is a coefficient?

 

 

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.

4

 

What is the leading coefficient?

 

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

5

How can you recognize that an equation is quadratic?

Some variable is squared. 

It can always be written as:

ax2+bx+c=0

6

What are the three ways to solve a quadratic equation?

  • Factorization
  • Completing the square
  • The quadratic formula

7

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

Vertex: (0,0)

Line of symmetry: x=0

8

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

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.

9

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

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.