Finding Maximum Values: Using Calculus to Solve Quadratic Equations

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To find the maximum value of the quadratic equation -3x^2 - 5x + 1, the turning point can be calculated using the formula -b/2a, which yields x = -0.8333. This value represents the x-coordinate of the maximum point, as the equation opens downward. The quadratic formula can also be used to determine the roots, and the maximum y-value is located at the midpoint of these roots. Completing the square is another method to find the maximum value. Understanding these techniques is essential for solving quadratic equations effectively.
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Question:
Hello, the question is to find the MAXIMUM VALUE of -3x^2-5x+1=0.

Attempt:

I tried to enter this into my calculate in Polynomial and got two values of x:
x=-1.85
and
x=0.1804

Thankyou!

See following post for attempted answer.
 
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ihopeican said:
Question:
Hello, the question is to find the MAXIMUM VALUE of -3x^2-5x+1=0.

Attempt:

I tried to enter this into my calculate in Polynomial and got two values of x:
x=-1.85
and
x=0.1804

Thankyou!

I came up with -0.8333333333.

I got this from thinking the maximum value is just the turning point (Ie: -b/2a)
 
Use the quadratic formula...
 
Using the quadratic formula to solve that equation will tell you where the value of y is 0. The x-value for maximum y will be halfway between the two roots.

By the way, you really want to find the maximum value of y= -3x^2-5x+1. An equation, like -3x^2-5x+1=0, doesn't have a "value" to begin with!

You can also find the maximum by completing the square in -3x^2-5x+1.
 
Hmm, read it wrong due to the zero... I agree that the equation doesn't have a value to begin with.
 
I used calculus to get the maximum, and I get what ihopeican got; x = -0.8333... without calculus, you can get the x value of the midpoint by -b/2a, as ihopeican suggested, or by finding the zeros of the equation and finding the average of their x values, as HallsofIvy suggested. When you get to calculus, you will learn how to use derivatives to get maximums and minimums of lots more equations, not just quadratics. It's fun, easy, and fast. XD
 
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