Question

I want to confirm my work. Thanks in advance for the help.

#1. Write the quadratic function in general form given that the function has an x-intercept of 6 and 1, and a y-intercept of 9.

x= 6, 1
y= 9
(0,9)

y=a(x-r1)(x-r2)
9=a(0-6)(0-1)
9=a(-6)(-1)
9=a(6)
a=3/2

y= 3/2(x-6)(x-1)
= 3/2(x^2-x-6x+6)
= 3/2(x^2-7x+6)
= (3/2x^2) - (21/2x) + 18/2

y= (3/2x^2) - (21/2x) + 9


#2. A small nerf gun was shot into the air by the function h(t) = 3(t-1)^2+2, where h is height and t is time.

How many seconds after it was fired did the nerf bullet hit the floor?

h(t) is 0 due to it landing, therefore there is no height.

0 =3(x-1)^2-4
=3x^2-6x-1

0 = -b ± √(b^2 - 4ac)/2a
= +6 ± √[-6^2 - 4(3)(-1)]/2(3)
= 2.15, -0.15

No negative time, therefore answer is 2.15 seconds.


#3. A cafe sells a cup of coffee for $3.00. The cafe sells around 800 cups per month. The poll shows that for every $0.50 increase in price, the cafe will sell 20 less cups of coffee. Find the price and number of cups sold that will maximise revenue.

R=(3.00+0.5x)(800-20x)
= 2400-60x+400x -10x^2
= -10x^2 + 340x +2400
= -10(x^2-34x)+2400
= -10(x-17)^2 +2400+2890
= -10(x-17)^2 +5290

Cups: 800-20(17)=460
Price: 3.00-0.5(2)=$11.5

Answer 1

#1 ok
#2 h(t) = 3(t-1)^2+2
is apparently a typo, but your solution is correct as written
#3 ok
if you ignore 3.00-0.5(2)=$11.5

good work