SOLUTION: Consider the following function. f(x) = 6x2 + 7x − 24 (a) Use the quadratic formula to find the zeros of f. (Enter your answers as a comma-separated list. If an answer does

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Question 845169: Consider the following function.
f(x) = 6x2 + 7x − 24
(a) Use the quadratic formula to find the zeros of f. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
x = Correct: Your answer is correct.
(b) Find the maximum or minimum value of f(x). (Round your answer to two decimal places.
Answer by pmesler(52)   (Show Source): You can put this solution on YOUR website!
By applying the quadratic formula to this equation 6x^2+7x-24 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=625 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1.5, -2.66666666666667. Here's your graph:


We get (-2.66, 0) and (1.5, 0) as the two roots.
The vertex of of the parabola that is formed from this equation is at the point
(-21, -26.04). Therefore the minimum value for f(x) is -26.04.
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