8. For the quadratic functions a. f(x) = -3z2 6x - 1, b. g(x) =2x1(a) Find the vertex form. What is the vertex? (b) Find the x and y intercepts of the above function.(c) Find the domain and the range(d) Find the maximum or the minimum.(e) Write a brief verbal description of the relationship between the graphof the above quadratic and the graph of h(x) x2.

Question
Asked Oct 17, 2019
2 views
8. For the quadratic functions a. f(x) = -3z2 6x - 1, b. g(x) =
2x1
(a) Find the vertex form. What is the vertex?
help_outline

Image Transcriptionclose

8. For the quadratic functions a. f(x) = -3z2 6x - 1, b. g(x) = 2x1 (a) Find the vertex form. What is the vertex?

fullscreen
(b) Find the x and y intercepts of the above function.
(c) Find the domain and the range
(d) Find the maximum or the minimum.
(e) Write a brief verbal description of the relationship between the graph
of the above quadratic and the graph of h(x) x2.
help_outline

Image Transcriptionclose

(b) Find the x and y intercepts of the above function. (c) Find the domain and the range (d) Find the maximum or the minimum. (e) Write a brief verbal description of the relationship between the graph of the above quadratic and the graph of h(x) x2.

fullscreen
check_circle

Expert Answer

Step 1

As per our policy I am solving 1st three subparts and for the remaining subparts post the question again separately.

Given,

-3x26x - 1 and g (x) = -x2 2x1
f(x)
help_outline

Image Transcriptionclose

-3x26x - 1 and g (x) = -x2 2x1 f(x)

fullscreen
Step 2

Part a

3x2 + 6x - 1
f (x)
-3(x2 — 2х) — 1
3(x2 2x
1 - 1) 1 (adding and subtracting 1)
- -3((x -1)2 -1) -1
— — 3 (х — 1)2 + 3 — 1
— — 3 (х — 1)2 + 2
So, the vertex form of f(x) is -3(x -1)2 2 and vertex of f(x) is (1,2)
help_outline

Image Transcriptionclose

3x2 + 6x - 1 f (x) -3(x2 — 2х) — 1 3(x2 2x 1 - 1) 1 (adding and subtracting 1) - -3((x -1)2 -1) -1 — — 3 (х — 1)2 + 3 — 1 — — 3 (х — 1)2 + 2 So, the vertex form of f(x) is -3(x -1)2 2 and vertex of f(x) is (1,2)

fullscreen
Step 3

And

...
g(x)-x2 - 2x + 1
- -(x2 2x)
1
-(x2 2x 1- 1)+ 1 (adding and subtracting 1)
((1)2 1) + 1
-(x + 1)2 + 1 +1
= -(x + 1)2 + 2
-(x + 1)2 2 and vertex of f (x) is (-1,2)
So, the vertex form of g (x) is
help_outline

Image Transcriptionclose

g(x)-x2 - 2x + 1 - -(x2 2x) 1 -(x2 2x 1- 1)+ 1 (adding and subtracting 1) ((1)2 1) + 1 -(x + 1)2 + 1 +1 = -(x + 1)2 + 2 -(x + 1)2 2 and vertex of f (x) is (-1,2) So, the vertex form of g (x) is

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Functions