Brainly doesn't automatically "know" every part of the problems you post here; you have to ensure that your post includes everything in the original problem.
We can still have some fun with answer choice <span>x = 1, x = 3:
An associated quadratic function would have the form y = a(x-1)(x-3). Just supposing that the point (2, 5) were on the graph, then this </span>y = a(x-1)(x-3) would become 5 = a(2-1)(2-3), or 5 = a(1)(-1), or 5 = -a, or a = -5.
Thus, the equation of the parabola would be y = -5(x-1)(x-3), or, in the more usual form, y = -5(x^2 - 4x + 3).
Complete the square to find the vertex:
Steal y = x^2 - 4x + 3 for a moment and complete the square:
x^2 - 4x + 3 = x^2 - 4x + 4 - 4 + 3, or (x-2)^2 - 1
Subbing this back into y = -5(x^2 - 4x + 3), we get
y = -5 [ (x-2)^2 -1 ], or y = -5(x-2)^2 + 5. This shows that the vertex is at (2, 5), that the graph opens downward, and the graph is symm. about the line x = 2.
Having fun yet?
Answer:
A
Step-by-step explanation:
Recall that for a quadratic equation of the form:
The number of solutions it has can be determined using its discriminant:
Where:
- If the discriminant is positive, we have two real solutions.
- If the discriminant is negative, we have no real solutions.
- And if the discriminant is zero, we have exactly one solution.
We have the equation:
Thus, <em>a</em> = 2, <em>b</em> = 5, and <em>c</em> = -<em>k</em>.
In order for the equation to have exactly one distinct solution, the discriminant must equal zero. Hence:
Substitute:
Solve for <em>k</em>. Simplify:
Solve:
Thus, our answer is indeed A.
Material=wall+2*side and material is 40 ft so:
40=w+2s
w=40-2s
Area=ws, using w from above we get:
A=(40-2s)s
A=40s-2s^2
dA/ds=40-4s and d2A/ds2=-4
Since d2A/ds2 is a constant negative acceleration, when dA/ds=0, A(s) is at an absolute maximum.
dA/ds=0 when 4s=40, s=10 ft
And since w=40-2s, w=20 ft
So the dimensions of the pen are 20 ft by 10 ft, with the 20 ft side being opposite the wall. And the maximum possible area is thus 200 ft^2
