Question

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)

Answer 1

@UsukiDoll this is the last one im having trouble with, can you help me? please

Answer 2

part A:
we have to solve the subsequent quadratic equation:
\[\Large - 16{x^2} + 22x + 3 = 0\]

Answer 3

can you help me with that? again im new to this...

Answer 4

I rewrite that equation as below:
\[\Large 16{x^2} - 22x - 3 = 0\]

Answer 5

Next I compare that equation with this more general equation:
\[\Large a{x^2} + bx + c = 0\]
so we can write:
a=16, b=-22, and c=-3
am I right?

Answer 6

yes

Answer 7

now, in order to find the requested x-intercepts, you have to apply this formula:
\[\Large x = \frac{{ - b \pm \sqrt {{b^2} - 4 \times a \times c} }}{{2 \times a}}\]
what do you get?

Answer 8

completely lost

Answer 9

you have to substitute the values of a, b, and c into that formula:
\[\Large \begin{gathered}
x = \frac{{ - b \pm \sqrt {{b^2} - 4 \times a \times c} }}{{2 \times a}} = \hfill \\
\hfill \\
= \frac{{ - \left( { - 22} \right) \pm \sqrt {{{\left( { - 22} \right)}^2} - 4 \times 16 \times \left( { - 3} \right)} }}{{2 \times 16}} = ...? \hfill \\
\end{gathered} \]

Answer 10

i dont have a calculator at the moment, its hard doing it in my head

Answer 11

please use windows calculator

Answer 12

\[\Large \begin{gathered}
x = \frac{{ - b \pm \sqrt {{b^2} - 4 \times a \times c} }}{{2 \times a}} = \hfill \\
\hfill \\
= \frac{{ - \left( { - 22} \right) \pm \sqrt {{{\left( { - 22} \right)}^2} - 4 \times 16 \times \left( { - 3} \right)} }}{{2 \times 16}} = \hfill \\
\hfill \\
= \frac{{22 \pm \sqrt {484 + 192} }}{{32}} = ...? \hfill \\
\end{gathered} \]

Answer 13

mine isnt working at the moment...

Answer 14

next step:
\[\Large \begin{gathered}
x = \frac{{ - b \pm \sqrt {{b^2} - 4 \times a \times c} }}{{2 \times a}} = \hfill \\
\hfill \\
= \frac{{ - \left( { - 22} \right) \pm \sqrt {{{\left( { - 22} \right)}^2} - 4 \times 16 \times \left( { - 3} \right)} }}{{2 \times 16}} = \hfill \\
\hfill \\
= \frac{{22 \pm \sqrt {484 + 192} }}{{32}} = \hfill \\
\hfill \\
= \frac{{22 \pm 26}}{{32}} = \begin{array}{*{20}{c}}
{\frac{{22 + 26}}{{32}} = ...?} \\
{\frac{{22 - 26}}{{32}} = ...?}
\end{array} \hfill \\
\end{gathered} \]

Answer 15

48/32 and -4/32

Answer 16

leaves you with -12/32

Answer 17

yes! and we can simplify them as below:
\[\Large {x_1} = \frac{{48}}{{32}} = \frac{3}{2},\quad {x_2} = - \frac{4}{{32}} = - \frac{1}{8}\]

Answer 18

what is -12/32?

Answer 19

your right, i was overr thinking..

Answer 20

so we got your x-intercepts

Answer 21

Now, part B:
the vertex of a parabola is the point at the top or the point at the bottom of a parabola

Answer 22

we have these subsequent cases: