Posted by **Laly** on Tuesday, July 13, 2010 at 6:31pm.

Please explain. I want to understand the steps.

1. A frog jumps from a rock to the shore of a pond. Its path is given by the equation y=(-5/72)x^2+(5/3)x, where x is the horizontal distance in inches, and y is the height in inches. What is the frog's maximum height? How far had it traveled horizontally when it reached its maximum height?

2. A local bakery determines that when the price of a package of cookies is $12, it sells on average 220 packages of cookies per day. For every $0.50 increase in the price, it sells on average 10 packages of cookies less. Determine the price that maximizes the bakery's profit. Determine the maximum profit.

3.Find the quadratic function with the vertex (7,10) and with point (10,28) on its graph.

- Pre-calc -
**Reiny**, Tuesday, July 13, 2010 at 8:17pm
looks like you are studying quadratic function.

You should have learned a method to find the vertex of such a funtion

here is a quick way

for y = ax^2 + bx + c

the x of the vertex is -b/(2a)

so in your case

x = (-5/3)/(-5/32) = 32/3

sub back in to get

y = 80/9

y is your height,

x is your horizontal distance

2. let the number of $0.50 increases be n

profit = (12 + .5n)(220 - 10n)

expand to get a quadratic, repeat the method I showed you in #1

3. let the function be

y = a(x-7)^2 + 10 , in the usual vertex form

but (10,28) lies on it

so 28 = a(10-7)^2 + 10

solve for a, and you got it

- Pre-calc -
**Leslie**, Tuesday, July 13, 2010 at 8:46pm
For 2 I did the function and got n=-1. then i substitute it in and got 11.5 is that the answer? if so to which of the 2 questions?

- Pre-calc -
**Reiny**, Tuesday, July 13, 2010 at 9:16pm
You are right, n = -1

Since I defined n as the number of .50 "increases" we have to interpret that as a "decrease" of 50 cents.

you can verify this by making a chart

cost - number - profit

12.00 220 ---- 2640

12.50 210 ---- 2625

11.50 230 ---- 2645

11.00 240 ---- 2640

etc

so the price should be $11.50, selling 230 of them for a maximum profit of $2645

btw, (11.5 , 2645) would be the vertex of your function

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