Quadratic Function?

Question

For the quadratic function f(x) = 5.93x^2 - 3.135x - 5.62, find the minimum or maximum value, the x-intercepts, and the y intercept.

1. Does this have a maximum or does it have a minimum value?

2. The x coords of the x intercepts are:

4. The Y intercept is:

Answer 1

1. Does this have a maximum or does it have a minimum value?
ANS : minimum value since +x^2

2. The x coords of the x intercepts are:
solve
5.93x^2 - 3.135x - 5.62 = 0
Use
Quadratic Formul
x = - b ± √ (b² - 4ac) / 2a


4. The Y intercept is:
Let x=0
y = 5.93(0)^2 - 3.135(0) - 5.62,
y= -6.62
(0,-5.62)

Answer 2

Hi,
1. Since the leading term, 5.93x^2 is positive, the hyperbola has a minimum. If that term were negative, the graph would be inverted and have a maximum. If you want to find the minimum point, find the x-coordinate from the expression:
x = -b/(2a) where b = -3.135 and a = 5.93. Then to find the y-coordinate, substitute that x-value into the original function.

2. Since the x-coordinates will not be whole numbers, you cannot factor this easily, so you will need to use the quadratic formula, or the Calc>zero function of a graphing calculator.
The quadratic formula is this:
x = [-b+-sqrt(b^2-4ac)]/2a Where a, b, and c are taken from the equation ax^2 +bx +c =0
In your problem, a = 5.93, b = -3.135, and c = -5.62. So, you can plug those numbers into the quadratic formula and do the arithmetic to get the x-intercepts.

3) To get the y-intercept, set the x-terms equal to zero.
f(x) = 5.93x^2 -3.135x - 5.62
f(0) = 5.93(0) -3.135(0) -5.62
= -5.62
So, y = -5.62 your y-intercept.

Hope this helps.
FE