Question

****FAN AND MEDAL FOR ANSWER******
An expression is shown below:

f(x) = -16x2 + 24x + 16

What are the x-intercepts of the graph of f(x)? Show your work.

Answer 1

@ganeshie8

Answer 2

if your trying to use the fancy leters dont worry about it ^ works just fine for me and its alot faster.

Answer 3

Result
−6x2+24x+16=−8(2x+1)(x−2)
Explanation
Factor out the GCF of −8.
−6x2+24x+16=−8(2x2−3x−2)
Now we need to factor 2x2−3x−2.
STEP1: Solve quadratic equation 2x2−3x−2=0
The solutions are:
x1=−12
x2=2
STEP2: Use formula for factoring quadratic equation:
ax2+bx+c=a(x−x1)(x−x2)
Where x1 and x2 are solutions of quadratic equation
In our case we have:
2x2−3x−2=2(x−(−12))(x−2) that is
2x2−3x−2=2(x+12)(x−2)
We can simplify this expression by multiplying the first bracket by 2.
After multiplying we have:
2x2−3x−2=(2x+1)(x−2)

Answer 4

Ohhhh, so then ax2+bx+c=a(x−x1)(x−x2) is the formula i would use in the future?

Answer 5

yes

Answer 6

there are 2 more parts to this, could you help me with thoes too?

Answer 7

sure

Answer 8

Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)

Answer 9

So you are going to use your original equation (-16x2+24x+16) and you are going t plug it in to the vertex equation: -b/2a.
So the equation becomes -24/2(-16) and you get: 0.75. Then you are going to plug 0.75 in for x and you get 25. So this means that the coordinates of the vertex. The vertex is also a minimum.

Answer 10

how would you then know the diffrence between a minimum and a maximum? does it have to with weather or not it is negative or positive?

Answer 11

You can tell by where the point is on the graph. So if the point negative it is a maximum and vice versa

Answer 12

oh ok
and then the last part of what i needed help with was
What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph

Answer 13

You would graph the vertex point. Then you would have to find the zeros(let me know if you need help with that). You would then graph those points and draw your line.

Answer 14

thank you very much :)

Answer 15

Welcome