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)

3 3 6, because in every triangle the longer side is always shorter than the sum of the other two

"standard form:

3x2 + 14x − 10 = 0

solutions based on quadratic formula:

x1   = −14 − √ 142 − 4×3×(−10) /   2×3   = −14 − 2 × √ 79 /   6   ≈ −5.296

x2   = −14 + √ 142 − 4×3×(−10) /   2×3   = −14 + 2 × √ 79 /   6   ≈ 0.629