An expression is shown below: f(x) = −16x2 + 22x + 3

Part A: What are the x-intercepts of the graph of the f(x)? Show your work. (2 points)

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)

Part C: 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. (5 points)

1. factor x intercepts  -1/8 , 3/2

2. vertex (11/16, 169/16) it is a maximum

3. graph the x intercepts and the vertex

Explaination:

putting the expression into the graph below:

Step 1.

Write -16x² + 22x + 3 as an equation.

y = -16x² + 22x + 3

Step 2.

Solve the equation,

Rewrite equation as:

-16x² + 22x + 3 = 0

Factor the left side of the equation.

Factor -1 out of -16x² + 22x + 3.

Factor -1 out of -16x², -(16x²) + 22x + 3 = 0

Factor -1 out of 22x, -(16x²) - (-22x) + 3 = 0

Rewrite 3 as -1 (-3), -(16x²) - (-22x) - 1 · -3 = 0

Factor -1 out of - (16x²) - (-22x), -(16x² - 22x) - 1 · -3 = 0

Factor -1 out of -(16x² - 22x) - 1 (-3), -(16x² - 22x - 3) = 0

For a polynomial of the form  ax² + bx + c, rewrite the middle term as a sum of two terms whose product is  a ⋅ c = 16 ⋅ -3 = -48 a ⋅ c = 16 ⋅ - 3 = - 48  and whose sum is  b = − 22.

Factor −22 out of −22x

-22x·16x2−22x−3=0

Rewrite −22-22 as 22 plus −24-2416x2+(2−24)x−3=0

Apply the distributive property.16x2+2x−24x−3=016x2+2x-24x-3=0

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.−((16x2+2x)−24x−3)=0

Factor out the greatest common factor (GCF) from each group.−(2 x(8x+1)−3(8x+1))=0

Factor the polynomial by factoring out the greatest common factor, 8x+18x+1.−((8x+1)(2x−3))=0

Remove unnecessary parentheses.−(8x+1)(2x−3)=0

Multiply each term in −(8x+1)(2x−3)=0-(8x+1)(2x-3)=0 by −1

16x²−22x−3=0

Factor by grouping.

(8x+1)(2x−3)=0(8x+1)(2x-3)=0

If any individual factor on the left side of the equation is equal to 00, the entire expression will be equal to 00.8x+1=08x+1=02x−3=02x-3=0

Set the first factor equal to 00 and solve.

x = -1/8

Set the next factor equal to 0 and solve.

x = 3/2

The final solution is all the values that make (8x+1)(2x−3)=0(8x+1)(2x-3)=0 true.

x = −1/8,3/2

y-intercept(s): (0,3)

List the intersections.x-intercept(s): (−1/8,0),(3/2,0)

y-intercept(s): (0,3)

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

1/800 is the right answer