1) what is the minimum value for g(x)=x^2−10x+16? enter your answer in the box.

2) what are the x-intercepts of the quadratic function? f(x)=x2−3x−10
enter your answers in the boxes. __and__

3) let f(x)=x2+17x+72 what are the zeros of the function?
enter your answers in the boxes.

4) let f(x)=x2+6x+11 . what is the minimum value of the function?
enter your answer in the box.

Part 1) The minimum value is

Part 2) The x-intercepts are -2 and 5

Part 3) The zeros of the function are -9 and -8

Part 4) The minimum value is

Step-by-step explanation:

Part 1) we have

we know that

The equation of a vertical parabola in vertex form is equal to

where

(h,k) is the vertex

if a>0---> the the parabola open upward (vertex is a minimum)

If a<0---> the the parabola open downward (vertex is a maximum)

Convert to vertex form

------> vertex form

The vertex is the point

the parabola open upward (vertex is a minimum)

Part 2) we have

we know that

The x-intercepts are the values of x when the value of the function is equal to zero

so

equate the equation to zero

The formula to solve a quadratic equation of the form is equal to

in this problem we have

so

substitute in the formula

Part 3) we have

we know that

The zeros of the function are the values of x when the value of the function is equal to zero

so

equate the equation to zero

The formula to solve a quadratic equation of the form is equal to

in this problem we have

so

substitute in the formula

Part 4) we have

we know that

The equation of a vertical parabola in vertex form is equal to

where

(h,k) is the vertex

if a>0---> the the parabola open upward (vertex is a minimum)

If a<0---> the the parabola open downward (vertex is a maximum)

Convert to vertex form

The vertex is the point

the parabola open upward (vertex is a minimum)

answer: just subtact the units and then add the non negative : happy to

step-by-step explanation: