Multiply out the "a times the squared coefficient" part on the left-hand side (remember, in this one a = 1 so that does nothing), and convert the right-hand side to squared form. (This is where you use that sign you kept track of earlier, putting that sign in the middle of the squared expression.)
y-4+(9)=(x+3)^2
Simplify - combine like terms.
y+5=(x+3)^2
Move the constant term from the right back to the left.
y=(x+3)^2 - 5
Write in vertex form y=(a(x-h)^2) + k. In other words, if the squared term is x+h write it as x-(-h). If the k term is negative, write it as + (-k).
y=(x-(-3))^2 + (-5)
Now the values for h and k are clear.I hope that this is the answer that you were looking for and it has helped you.
<span>A.
Both functions have the same y-intercept.</span> TRUE
<span>B.
f(x) has a negative slope while g(x) has a positive slope.</span> Tricky question. Yes, f(x) has the negative slope m = -2. However, g(x), being a curve, does not have a single slope; rather, it has a varying slope that increases (becomes less negative) as x increases. Some people might argue that this statement is TRUE, while others would argue that it's FALSE, because the 2nd function does not have just one single value for the slope.
<span>C.
Both functions are linear functions.</span> ABSOLUTELY NOT. The first one is linear; the second is a "decaying exponential" whose graph is a curve.
D. <span>
g(x) has a common ratio of 4. Yes and no. I'd say the common ratio is (1/4), because each y value is (1/4) of the previous y value
</span>
Let
x--------> the border’s length
y--------> the border’s width
P--------> perimeter of the border
we know that
x=5+y------> equation 1
P=2*[x+y]-----> P=2x+2y
P <=180 ft
(2x+2y) <= 180-------> equation 2
substitute the equation 1 in equation 2
2*[5+y]+2y <= 180
10+2y+2y <= 180
4y <= 180-10
4y <=170
y <=42.5 ft
so
the maximum value of the width is 42.5 ft
for y=42.5 ft
x=42.5+5------> x=47.5 ft
the answer is
the width of the border is less than or equal to 42.5 ft
Answer:
She spent 4 $10 bills and 3 $1 bills
Step-by-step explanation:
She used 7 bills and you have 3 $1 that makes the 3 of 43 then 4 $10 bills adds up to 40 so add 40 and 3 together you get the price of the shoes and if you add the 4 $10 bills and the 3 $1 bills you get 7
Answer:
Step-by-step explanation:
The first parabola has vertex (-1, 0) and y-intercept (0, 1).
We plug these values into the given vertex form equation of a parabola:
y - k = a(x - h)^2 becomes
y - 0 = a(x + 1)^2
Next, we subst. the coordinates of the y-intercept (0, 1) into the above, obtaining:
1 = a(0 + 1)^2, and from this we know that a = 1. Thus, the equation of the first parabola is
y = (x + 1)^2
Second parabola: We follow essentially the same approach. Identify the vertex and the two horizontal intercepts. They are:
vertex: (1, 4)
x-intercepts: (-1, 0) and (3, 0)
Subbing these values into y - k = a(x - h)^2, we obtain:
0 - 4 = a(3 - 1)^2, or
-4 = a(2)². This yields a = -1.
Then the desired equation of the parabola is
y - 4 = -(x - 1)^2
