Well, to find the vertex of a quadratic, we have a few options. we can either complete the square, or solve for the x value of the vertex using a nifty equation. I'm gonna go that route, but if your interested in the complete the square thing I can show you.
Anyway, the x value of a vertex equals
x = -b/2a
assuming
f (x) = ax^2 + bx + c.
so b is the coefficient in front of just x and a the coefficient in front of x^2 and so on. let's solve for x in your problem.
y = 4x^2 + bx + c
so, our x value has to be
x = -b/2 (4) right? so how do we solve for b, which is what we wanna know, from that? well, we KNOW the x value is supposed to be -7 in this case. so that means...
-7 = -b/2 (4) now just solve for b.
b = 56 if you need the work I can show you in comments.
Anyway, now we know b. how do we solve for c? well, let's fill in our old equation with our new info.
y = 4x^2 + 56x + c
what do we know? well, we know the vertex of this line is (-7,6). what does this tell us? well, the vertex is a point on our line, so that means I could plug in my point, right?
6 = 4 (-7)^2 + 56 (-7) + c
if (-7,6) is a point on my line, ^^^ that will be true. now all you gotta do is solve for c. if you need the work, I can show ya in the comments.
c = -196
hope this helps!
<h2>
Time required to complete the round trip where x is average velocity on the outgoing trip.</h2>
Step-by-step explanation:
Let average velocity of outgoing trip = x mph
The average velocity on the return trip is 15 miles per hour slower than the average velocity on the outgoing trip.
Average velocity of return trip = (x-15) mph
Distance to vacation place = 420 miles
Distance to vacation place = Time for outgoing trip x average velocity of outgoing trip
Distance to vacation place = Time for return trip x average velocity of return trip
We have total time T = t₁ + t₂
That is
Time required to complete the round trip where x is average velocity on the outgoing trip.
This is probably wrong but 11w (like saying 11 times w)
If the "break apart stradegy" is the same as what I was taught, you would add the ones place, the tens place, the hundreds place, and so on. This would be 7 + 8 then 40 + 50 and then 200 + 300. Add what you got together. So 247 + 358. You would get 605.