The equation of parabola becomes y = -2/25(x-3)^2 + 4.
According to the statement
we have given a graph and from this graph we have to find the equation of parabola in the general form.
So,
we know that the equation of parabola in general form is
y = a(x-h)^2 +k - (1)
From the graph we have:
a point on the graph is (x,y) = (-2,2)
the vertex of the graph is (h,k) = (3,4)
Now, substitute these values in the equation number (1)
Then
y = a(x-h)^2 +k
2 = a(-2-3)^2 +4
2 = a(-5)^2 +4
2 = a(25) +4
25a = -2
a = -2/25.
Now put a = -2/25 and (h,k) = (3,4) in the equation(1).
Then
the equation of parabola becomes y = -2/25(x-3)^2 + 4
So, The equation of parabola becomes y = -2/25(x-3)^2 + 4.
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We factor the equation to get:
-(x-25)^2+361
In the form a(x-h)^2+k, the vertex is (h, k), so the vertex is (25, 361). This means that the studio makes the most profit from selling 25 memberships, and thus makes 361 dollars.
B. The x-intercepts are the values of x for which f(x) is 0. This equation can be factored as (-a+6)(a-44)=0, with solutions 6 and 44. Therefore, by selling either 6 memberships or 44 memberships, the studio breaks even, neither making nor losing money.
Answer:
The graph of a linear equation is a straight line. The "solution" to a system of two linear equations is the point where the two lines cross. If the two lines are parallel, they never cross; hence parallel lines have no solution. Two lines are parallel if they have the same slope (the m value in y = mx+b). One of your equations is y = -2x + (you left the y-intercept out). The slope is -2. So any line with a slope of m = -2 will be parallel to this line and will not cross it. The second line also needs a different value of b, the y-intercept. Otherwise it is the same line and every point is a solution. So if your equation is:
y = -2x + 1
Then any equation of the form y = -2x + b, b≠1 will create a system with no solution. Hence the values of m and b are m = -2, b ≠ 1.
9/10 - 5/10
because the denominators are the same you keep it and just subtract the numerators
=4/10
This can be reduced to 2/5
