Find the minimum or maximum value of each function. then State the domain and range of the function. 1. g(x)=x^2-2x+1 2.h(x)= 5x^2+ 15x-3

1.

The minimum value of g(x) is (1 , 0)

The domain of g(x) is {x : x ∈ R}

The range of g(x) is {y : y ≥ 0}

2.

The minimum value of h(x) is (-1.5 , -14.25)

The domain of h(x) is {x : x ∈ R}

The range of h(x) is {y : y ≥ -14.25}

Step-by-step explanation:

The quadratic function f(x) = ax² + bx + c is represented graphically by a parabola which has a minimum/maximum vertex (h , k), where

Now let us solve the problems

1.

∵ g(x) = x² - 2x + 1

∵ The form of the quadratic function is f(x) = ax² + bx + c

∴ a = 1 , b = -2 , c = 1

∵ a is positive

∴ The function has a minimum value

∵ h =

∴ h =

- To find k substitute x in g(x) by 1

∴ g(1) = (1)² - 2(1) + 1 = 1 - 2 + 1

∴ g(1) = 0

∵ k = g(h)

∴ k = 0

∴ The minimum value of g(x) is (1 , 0)

∵ The domain of the quadratic function is all real numbers

∴ The domain of g(x) is {x : x ∈ R}

∵ The range of the quadratic function with minimum value is

   {y : y ≥ k}

∴ The range of g(x) is {y : y ≥ 0}

2.

∵ h(x) = 5x² + 15x - 3

∴ a = 5 , b = 15 , c = -3

∵ a is positive

∴ The function has a minimum value

∵ h =

∴ h =

∴ h = - 1.5

- To find k substitute x in h(x) by 1

∴ h(-1.5) = 5(-1.5)² + 15 (-1.5) - 3 = 11.25 - 22.5 - 3

∴ h(-1.5) = -14.25

∵ k = h(h)

∴ k = -14.25

∴ The minimum value of h(x) is (-1.5 , -14.25)

∵ The domain of the quadratic function is all real numbers

∴ The domain of h(x) is {x : x ∈ R}

∵ The range of the quadratic function with minimum value is

   {y : y ≥ k}

∴ The range of h(x) is {y : y ≥ -14.25}

the circle one

answer is:

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