Test each
if angle is increased, rock will go further
if the angle starts at 0, then increases to 90 degrees (straight up) the rock will go up then bounce off of the launcher going either front or back, but vastly shorter than if it were pointed straight ahead
2nd one
changing angle change the distance
we see that is true
So you need to come up with a perfect square that works for the x coefficients.
like.. (2x + 2)^2
(2x+2)(2x+2) = 4x^2 + 8x + 4
Compare this to the equation given. Our perfect square has +4 instead of +23. The difference is: 23 - 4 = 19
I'm going to assume the given equation equals zero..
So, If we add subtract 19 from both sides of the equation we get the perfect square.
4x^2 + 8x + 23 - 19 = 0 - 19
4x^2 + 8x + 4 = - 19
complete the square and move 19 over..
(2x+2)^2 + 19 = 0
factor the 2 out becomes 2^2 = 4
ANSWER: 4(x+1)^2 + 19 = 0
for a short cut, the standard equation
ax^2 + bx + c = 0 becomes a(x - h)^2 + k = 0
Where "a, b, c" are the same and ..
h = -b/(2a)
k = c - b^2/(4a)
Vertex = (h, k)
this will be a minimum point when "a" is positive upward facing parabola and a maximum point when "a" is negative downward facing parabola.
You didn’t add a picture, so it’s impossible to answer
Answer:
The answer is: y = 3x - 7
Step-by-step explanation:
Given point: (5, 8).
Slope m = 3
Use the point slope form and solve for y:
y - y1 = m(x - x1)
y - 8 = 3(x - 5)
y - 8 = 3x - 15
y = 3x - 15 + 8
y = 3x - 7
Proof:
f(x) = 3x - 7
f(5) = 3(5) - 7
= 15 - 7 = 8, giving (5, 8)
When you owe money it is a negative because when you earn money you have to pay it back
