Question

Need help will medal topic is solving quadratic functions

Answer 1

Last one #22

Answer 2

you are given the v0 and s0
plug those in

Answer 3

\[h(t)=-16t^2+4t+10\]

to find the max, find the vertex

Answer 4

@freckles ok one second let me find the vertex

Answer 5

@freckles ok I need help I can't figure it out

Answer 6

k

Answer 7

@freckles will you help?

Answer 8

\[y=ax^2+bx+c \\ \text{ we are going to put this in the form } \\ y=a(x-h)^2+k \\ \]
\[ \text{ So to makes things easier for you to see I'm going to multiply second term by } \frac{a}{a} \\ y=ax^2+bx+c \\ y=ax^2+\frac{a}{a}bx+c \\ \text{ Now from the first two terms I'm going to factor out a } a \\ y=a(x^2+\frac{1}{a}bx)+c \\ \text{ Now for completing the square } \\ y=a(x^2+\frac{b}{a}x+(\frac{b}{2a})^2)+c-a (\frac{b}{2a})^2 \\ \text{ Notice here I added in a zero to complete the square } \\ \text{ that zero being } a (\frac{b}{2a})^2-a(\frac{b}{2a})^2 \\ \text{ now we can write this think as } \\ y=a(x+\frac{b}{2a})^2+c-a(\frac{b}{2a})^2\]
So this in vertex form and the vertex is :
\[(-\frac{b}{2a},c-a(\frac{b}{2a})^2)\]

Answer 9

what people usually this is calculate the x-coordinate of the vertex which is -b/(2a)
then they plug into the original function so they don't have to remember the extra there...
\[(-\frac{b}{2a},f(-\frac{b}{2a}))\]

Answer 10

where
\[f(x)=ax^2+bx+c\]

Answer 11

So anyways see if you can find the x-coordinate now.

Answer 12

(1/8, 41/4) @freckles

Answer 13

yes that is what I have gotten

Answer 14

now the 1/8 says when the max happens
41/4 says what the max is

Answer 15

and I guess you should say 41/4 ft
(including units make you awesome and more correct)

Answer 16

So let restate what I said (with the units)
now 1/8 secs is when the max happens
41/4 ft is what the max is

Answer 17

Wait what? @freckles

Answer 18

the vertex is the maximum point
the t-coordinate is where the max occurs
the h-coordinate is what the max is
I was just saying you may want to include units also

Answer 19

t-coordinate is in seconds units
h-coordinate is in feet units

Answer 20

Okay so what would I put for my answer ? @freckles

Answer 21

hint: the question is asking for the maximum height

Answer 22

and I actually already said what this was above

Answer 23

1/8t or X=1/8? @freckles