Given the quadratic function f(x)=3x^2-24x+49 a. use “completing the squares” to convert the quadratic function into vertex form b. state the vertex c. find the x and y intercepts d. graph the function

See below.

Step-by-step explanation:

A.  F(x)=3x^2 - 24x + 49

f(x) = 3(x^2 - 8x) + 49

f(x) = 3 [(x - 4)^2 - 16]  + 49

f(x) = 3(x - 4)^2 - 48 + 49

f(x) =  3(x - 4)^2 + 1  < Vertex form. (answer).

B.

The vertex is at (4, 1). (answer).

C.

The y-intercept occurs when x = 0:

y = 3(0- 4)^2 + 1

= 3*16 + 1

= 49

The y-intercept is at (0, 49). (answer)

The x intercepts occur when y = 0:

3(x - 4)^2 + 1 = 0

3(x - 4)^2 = -1

(x - 4)^2 = -1/3

Since there is no real square root of a negative there are no x-intercepts.

(Answer)

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)  

6 cm

step-by-step explanation: