determine whether the quadratic function shown below has a minimum or maximum, then determine the minimum or maximum value of the function

Question

f(x)=x^2-6x+14

Answer 1

f(x) = x² - 6x + 14

The graph of the function is a parabola opening upward (because the coefficient of x² is positive). Therefore, the function has a minimum value.

The minimum or maximum of a quadratic function f(x) = Ax² + Bx + C occurs when x = -B/(2A).

So, for the given function, x = -B/(2A) = 6/2 = 3 is the x-coordinate of the lowest point on the graph.

Minimum value = f(3) = 5

Answer 2

Hi River R

f(x) = x^2-6x+14

Is a standard form parabola ax² + bx + c

Where a = 1, b = -6 and c = 14

f(x) = x² -6x + 14

Since a = 1 it opens upward and has a minimum at its vertex

The x coordinate of the vertex -b/2a = -(-6)/2 = 3

The y coordinate of the vertex can be found by plugging in the x coordinate

f(3) = 3² - 6(3) + 14 = 9 - 18 + 14 = 9 - 4 = 5

So the vertex is at (3, 5)

The y intercept is (0, 14)

It does not touch the x axis and has no x intercepts you can use the Quadratic Formula to check this out and you can plot your function at Desmos.com