For the quadratic function f(x)= 5.92x^2 - 3.135x -5.86, find the max or min value, x intercpts, and y intrcpt

Answer 1

The y-intercept is -5.86, by inspection.

From the quadratic formula:

x = [3.135 +/- sqrt(3.135^2 + 4*5.92*5.86)] / (2*5.92)

x = (3.135 +/- 12.190) / 11.84

x = 1.294 or x = -0.765

(These are the roots.)

The minimum is at x = 3.135 / 11.84 = 0.265

and its value is y = -6.275

Min at (0.265, -6.275) if you like it that way.

Answer 2

think you have a quadratic equation of the form y = ax² + bx + c the place a is beneficial. Then rewrite it as under. => y = a(x² + (b/a)x + c/a) => y = a [ (x + b/2a)² - b²/4a² + c/a ] => y = a [ (x + b/2a)² - (b²/4a² - c/a) ] Now y is minimum while x + b/2a = 0 and the minimum fee is a [-b²/4a² + c/a] which will properly be beneficial or detrimental. If the quadratic equation is y = - ax² + bx + c, the place a is beneficial yet first term is -ax² => y = - a [ x² - bx/a - c/a ] => y = a [ - (x - b/2a)² + b²/4a² + c/a ] right here, y would be optimum while x - b/2a = 0 and the optimum fee is - a [ b²/4a² + c/a ] Summarizing, you are able to endure in ideas a formulation that once a is beneficial, y is minimum and the minimum fee is - a [b²/4a² - c/a] and while a is detrimental, y is optimum and the optimum fee is - a [b²/4a² + c/a].

Answer 3

without calculations the equation is a minimum graph because the coefficient of x^2 is +ve.
the minimum point is found by using -b/2a
=-b/2a = -(-3.135)/2 x 5.920 =0.265
y value of the min point is 5.920(0.265)^2 - 3.135(0.265) - 5.860
=0.415.435-0.83078-5.860
= - 6.276
min point (0.265,-6.276)
x intercept is the point where f(x) = zero
5.92x^2 -3.135x - 5.86 = 0
5920x^2 - 3135x - 5860 = 0
solve quadratically if
y intercept is the point where x = 0
= - 5.86
i hope i have helped

Answer 4

The y-intercept is -5.86, by inspection.

From the quadratic formula:

x= a+/-(sqrt(b^2-4*a*c)/2*a)

x = [3.135 +/- sqrt(3.135^2 + 4*5.92*5.86)] / (2*5.92)

x = (3.135 +/- 12.190) / 11.84

x = 1.294 or x = -0.765

(These are the roots.)

The minimum is at x = 3.135 / 11.84 = 0.265

and its value is y = -6.275

Min at (0.265, -6.275) if you like it that way.

Answer 5

min is (.26478,-6.27504), max is all real value. x intercept is when X=0, so set the x's equal to 0 . y intercept is when y =0 so use the quadratic formua.

Answer 6

differentiating
11.84x-3.135=0
x=3.135/11.84
=0.27
d^2y/dx^2=11.84
=+ve so minimum at x=0.27
y intercept=(0,-5.86)
putting y=0 and solving you
wiil get he 'x' intercept

Answer 7

Just put it in your graphing caluclator. The answers come right out.