Mathematics, 02.07.2019 08:20 fatboicroi

The axis of symmetry for the function f(x) = −x2 − 10x + 16 is x = −5. what are the coordinates of the vertex of the graph? (−5, 41) (−5, 56) (−5, 76) (−5, 91)

Answers: 2

Show answers

Answers

Considering the definition of axis of symmetry and vertex of a quadratic function, the correct answer is the first option: the coordinates of the vertex of the graph is (-5,41).

Quadratic function

The general form of a quadratic function is f(x = ax²+ bx+ c, whose graph is a parabola.

Axis of symmetry and vertex of a quadratic function

Quadratic functions have a maximum (if a<0) or a minimum (if a>0). This point is the vertex of the parabola.

That is, the vertex of a quadratic equation or parabola is the highest or lowest point on the graph corresponding to that function. The vertex is in the plane of symmetry of the parabola; anything that happens to the left of this point will be an exact reflection of what happens to the right.

In other words, the vertex divides the graph into two halves that are mirror images of each other, so that the axis of symmetry always passes through the vertex.

Vertex of f(x) = −x² − 10x + 16

In this case, you know that the axis of symmetry for the function is x = −5.

So the vertex on the x-axis has a value of -5. To calculate the value of the vertex on the y-axis, you must substitute the value of the vertex on the x-axis in the function:

f(-5) = −(-5)² − 10×(-5) + 16

Solving:

f(-5)= 41

In summary, the correct answer is the first option: the coordinates of the vertex of the graph is (-5,41).

Learn more about the vertex of a quadratic function:

link

Answer from: plutoaliko99

we know that

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

$y=a(x-h)^{2} +k$

where

(h,k) is the vertex

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

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

In a vertical parabola the axis of symmetry is equal to

x=h

In this problem we have

$f(x)=-x^{2}-10x+16$

Complete the square

$f(x)-16=-(x^{2}+10x)$

$f(x)-16-25=-(x^{2}+10x+25)$

$f(x)-41=-(x+5)^{2}$

$f(x)=-(x+5)^{2}+41$

The parabola open downward

the vertex is the point (-5,41) (is a maximum)

therefore

the answer is

(-5,41)

Answer from: Quest

a=r

d=q

c=p

b=s

hope this !

The two figure shown above are congruent. identify the corresponding sides and angles.

Answer from: Quest

step-by-step explanation:

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 18:30, povijuaisaiah

Use δjkl and δmpn to determine whether don's claim is true or false. which of the following should don use to prove the triangles are similar? sss sas aas aa

Answers: 1

continue

Mathematics, 21.06.2019 20:30, savannahvargas512

For g(x) = 5x - 3 and h(x) = [tex]\sqrt{x}[/tex], find (g · h)(4)

Answers: 1

continue

Mathematics, 21.06.2019 23:10, funmi5504

Proportions in triangles solve for x

Answers: 3

continue

Mathematics, 21.06.2019 23:50, jasminer257

Mariah is randomly choosing three books to read from the following: 5 mysteries, 7 biographies, and 8 science fiction novels. which of these statements are true? check all that apply. there are 20c3 possible ways to choose three books to read. there are 5c3 possible ways to choose three mysteries to read. there are 15c3 possible ways to choose three books that are not all mysteries. the probability that mariah will choose 3 mysteries can be expressed as . the probability that mariah will not choose all mysteries can be expressed as 1 −

Answers: 1

continue

You know the right answer?

The axis of symmetry for the function f(x) = −x2 − 10x + 16 is x = −5. what are the coordinates of t...