Answer:
Plot and connect (5,4), (3,0) and (7,0).
Step-by-step explanation:
This is in factored form and can be graphed directly from the equation. The equation shows the x-intercepts.
The x-intercepts are found by solving for x using the zero product rule.
(x-3)=0 so x = 3
(x-7) = 0 so x = 7
The intercepts are (3,0) and (7,0). Plot the points. The vertex will occur halfway between these points. 7-3 / 2 = 4/2 = 2. This means the axis of symmetry is at x = 5 and this is the x-coordinate of the vertex too.
Substitute x = 5 into the equation and solve for y.
-(5-3)(5-7) = -(2)(-2) = 4
The vertex is (5,4). Plot it and connect the points.
Answer:
what do you need I'm not the smartest person but I may be able to help :)
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:
the limit does not exist
Step-by-step explanation:
As x approaches π/2 from below, tan(x) approaches +∞. A x approaches π/2 from above, tan(x) approaches -∞. These two limits are not the same, so the limit is said not to exist.
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For a limit to exist, it must be the same regardless of the direction of approach.
