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.
Answer:
1a expression
1b equation
1c equation
1d expression
1e expression
1f equation
Step-by-step explanation:
Equations have an equals sign, expressions do not
1a expression
1b equation
1c equation
1d expression
1e expression
1f equation
Answer:
x = 0.5
Step-by-step explanation:
For the first option, since when x is going down (to the left) the function is going up, it's not approaching 0. For the second option, since when x is going up (to the right) it's going up, it's not approaching negative infinity (negative infinity is all the way down). For the third one, since when x is going down the y values are climbing, we can assume that the function's values go to positive infinity. For the last one, since when x=0 y=0, when x=0 the function does not go to infinity
Answer:
Where is the question?
Step-by-step explanation:
please attach it...
