Answer:
y = - x² - 15x - 56
Step-by-step explanation:
y = - (x + 8)(x + 7) ← expand factors using FOIL
= - (x² + 15x + 56) ← distribute parenthesis by - 1
y = - x² - 15x - 56 ← in standard form
I can’t comment but good luck. It looks like a practice problem.
Answer:
5 gallons
Step-by-step explanation:
We can use ratios to solve
5/12 gallon x gallons
---------------- = -------------------
1/24 minute 1/2 minute
Using cross products
5/12 * 1/2 = x *1/24
5/24 = x/24
Multiply each side by 24
24*5/24 = x/24*24
5=x
We can pump 5 gallons
We know that the graph goes in units of 1.
We know that the roots are -1 and 4. (Just assume it's accurate and not off by 0.0000000001.)
We can set it up as an equation: -1(x+1)(x-4) = y (I added -1 because there are two parabolas that go through those points on the x-axis, and since this parabola is facing down, I must add a negative a value.
Then multiply (F.O.I.L. - First, Outer, Inner, Last)
x^2 -4x + x - 4 = -(x^2 - 3x - 4) = -x^2 + 3x + 4
Then using -(b/2a) solve for vertex: -(3/-2) = 3/2
Plug 3/2 back into the equation.
-(3/2)^2 + 3(3/2) + 4 = -9/4 + (9/2) + 4 = 25/4
The vertex would be: (3/2, 25/4)
Axis of symmetry would be: x = 3/2
