What is a quadratic?

The general quadratic looks like:

**ax ^{2} + bx + c**

"Quad" means "square", which in math means to the power of 2. So a quadratic is an equation that contains an x^{2}, and this is the highest power. There can't be, for example x^{3}, nor x^{4}, and so on. Only the square is the highest power. Quadratic expression contains *three terms*, which makes it a **trinomial**.

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. 3x^{2} + 4x + **7**

**7 is the constant**.

3 and 4 are coefficients.

3 is the leading coefficient.

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.

**3**x^{2} + **2**x - 4

3 is the coefficient of x^{2},

and 2 is the coefficient of x.

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

**4**x^{2} + 3x + 9

the leading coefficinent is **4**

How can you recognize that an equation is quadratic?

Some variable is squared.

It can always be written as:

ax^{2}+bx+c=0

What are the three ways to solve a quadratic equation?

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- Factorization
- Completing the square
- The quadratic formula

What does the graph of f(x)=x^{2} look like? What are the vertex and line of symmetry?

Vertex: (0,0)

Line of symmetry: x=0

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.

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.