Question

Graphing Quadratic Functions (help please )

Find the vertex and zeros of each graph, then make a graph of each function. Label the vertex and zeros of each graph.

1. f(x) = - 2(x - 4) (x + 6). 4. Y = -(x - 4)^2 + 11
Vertex = _______
Zeros = _______
Vertex = _______

Zeros = _______


2. Y= 3(x + 1)(x + 6)

Vertex =_______
Zeros =_______


3. Y= -2(x - 4) (x + 6)

Vertex =______

Zeros =_______

Answer 1

#1

Zeroes: x = 4, x = -6

The vertex is at ( -1 , 50 )

Explanation:

I'll do the first one, you try the rest

All of these are written in y = a(x - x1)(x - x2) where x1 and x2 are given and x are the two different zeroes (or x-intercepts)

f(x) = -2(x-4)(x+6)

The zeroes are x - 4 = 0 and x + 6 = 0 if you solve, you get 4 and -6

Zeroes: x = 4, x = -6

The x value of the vertex can be found using -b/2a (in the form ax^2 + bx + c)

First expand f(x)

-2(x^2 + 2x - 24) => -2x^2 - 4x + 48

b = -4 and a = -2

-(-4)/2(-2) = 4/-4 = -1

the x-value of the vertex is -1

Now substitute -1 as x to find the y-value of the vertex

-2(-1-4)(-1+6) = -2(-5)(5) = 50 <= y-value of vertex

The vertex is at ( -1 , 50 )