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#mathematics
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#equation-solving
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Without using table draw the graph of f(X)=-x^2+4x_5 and use it to solve -x^2+4x_5=10?

Feb 22

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Feb 22

To graph the function f(x) = -x^2 + 4x + 5, we can first find the vertex of the parabola by using the formula x = -b/2a. In this case, a = -1 and b = 4, so the vertex occurs at x = -4/(2*-1) = 2.

Next, we can find the y-coordinate of the vertex by plugging x = 2 into the function: f(2) = -2^2 + 4(2) + 5 = -4 + 8 + 5 = 9.

So the vertex of the parabola is at (2, 9).

To solve the equation -x^2 + 4x + 5 = 10, we can set the function equal to 10 and solve for x:

-x^2 + 4x + 5 = 10

-x^2 + 4x - 5 = 0

Now we can factor the quadratic equation:

-(x - 5)(x + 1) = 0

Setting each factor equal to zero gives us the solutions x = 5 and x = -1.

Therefore, the solutions to the equation -x^2 + 4x + 5 = 10 are x = 5 and x = -1.

Next, we can find the y-coordinate of the vertex by plugging x = 2 into the function: f(2) = -2^2 + 4(2) + 5 = -4 + 8 + 5 = 9.

So the vertex of the parabola is at (2, 9).

To solve the equation -x^2 + 4x + 5 = 10, we can set the function equal to 10 and solve for x:

-x^2 + 4x + 5 = 10

-x^2 + 4x - 5 = 0

Now we can factor the quadratic equation:

-(x - 5)(x + 1) = 0

Setting each factor equal to zero gives us the solutions x = 5 and x = -1.

Therefore, the solutions to the equation -x^2 + 4x + 5 = 10 are x = 5 and x = -1.