graphing quadratics

Question

-3(x-6)^2+3 x values from 2 to 10 

b) what is the vertex
c) what is the x-intercept
d) what is the y-intercept
e) factor the expression
f) what is the equation in vertex form

Answer 1

b)

 

The vertex is the turning point of the parabola.  The vertex form of a parabola is

 

y = a(x - h)² + k

 

where:

a is the coefficient of the x² term

vertex is the coordinate (h, k)

 

h = 6

k = 3

 

The vertex is then (6, 3). 

 

 

c)

 

To find the x-intercept, we set the function equal to zero and solve for x.

 

0 = -3(x - 6)² + 3

 

-3 = -3(x - 6)²

 

1 = (x - 6)²

 

±√1 = x - 6

 

±1 = x - 6

 

 

-1 + 6 = x                 and                1 + 6 = x

 

 

Solve the two parts to get the x-intercepts.

 

 

d)

 

To find the y-intercept, we set we evaluate the function when x=0.

 

 

e)

 

To factor, we can expand what is left.

 

-3(x - 6)(x - 6) + 3 =

 

-3(x² - 12x + 36) + 3 =

 

-3x² + 36x - 108 + 3 =

 

-3x² + 36x - 105 =

 

-3(x² - 12x + 35) =

 

-3(x - 7)(x - 5)

 

 

f)

 

The equation is already in vertex form.