nc math 2 unit 5

Linear graph

Quadratic graph

Exponential graph

What is the formula for the y-intercept of a quadratic in standard form f(x)=ax^2+bx+c

The y-intercept is (0, c)

How do you find the y-intercept in factored form f(x)=a(x-p)(x-q)?

Plug in x=0. The y-intercept is (0, a x p x q)

How do you find the x-intercepts from factored form?

Set each factor equal to zero. x=p and x=q

Points: (p,0), (q,0).

What is the formula for the line of symmetry in factored form f(x)=a(x-p)(x-q)?

R= p+q/2 (the average of the roots).

How do you find the line of symmetry in standard form ax^2+bx+c?

X= -b/2a

How do you find the vertex if you know the line of symmetry?

Plug the symmetry line (x-value) into the equation to find the y-value. Vertex is (h, f(h)).

standard form f(x)=ax^2+bx+c, what is the formula for the vertex?

Vertex: (-b/2a, f(-b/2a))

How can you tell if a parabola opens up or down?

Look at a (the coefficient of x^2).

• If a>0, opens up.

• If a<0, opens down.

How do you change from factored form to standard form?

Multiply the factors out (expand). Example: (x+3)(x-3)=x^2-9.

What is the general shape of the graph of a quadratic?

A parabola (a “U”-shaped curve).

c

Y intercept

P,q

X intercept

H,k

The vertex