Mathematics, 15.07.2019 04:10 bigblow

F(x)=x^2+9x-16
what is vertex
axis of semetry

Answers: 2

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Answer from: mccdp55

axis of symmetry is $x=\frac{-9}{2}$ .

The ordered pair of the vertex is $(\frac{-9}{2},\frac{-145}{4})$ .

Step-by-step explanation:

Your function is a quadratic.

Compare x^2+9x-16 to ax^2+bx+c .

You should see that a=1,b=9,c=-16 .

The x-coordinate of the vertex or the axis of symmetry since the axis symmetry goes through the vertex can be found by computing $\frac{-b}{2a}$ .

So here we go!

The axis of symmetry is $x=\frac{-9}{2(1)}=\frac{-9}{2}$ .

When you write your axis of symmetry be sure to write it as an equation.

That is the axis of symmetry is $x=\frac{-9}{2}$ .

Now that was also the x-coordinate of your vertex. To find the corresponding y-coordinate of the vertex, plug your value for into

y=x^2+9x-16 .

$y=(\frac{-9}{2})^2+9(\frac{-9}{2})-16$

Put into calculator:

$y=\frac{-145}{4}$ when $x=\frac{-9}{2}$

The ordered pair of the vertex is $(\frac{-9}{2},\frac{-145}{4})$ .

Answer from: brittanyjacob8

Vertex: $(h,k)\rightarrow(-4.5,-36.25)$

Axis of symmetry: x=-4.5

Step-by-step explanation:

Finding the Axis of Symmetry:

First I'll find the axis of symmetry. This formula lets us find the a.o.s: $x=\frac{-b}{2a}$ .

In x^2+9x-16 , the values of a, b, and c are:

a: 1b: 9c: -16

We only need a and b to find the axis of symmetry. Substitute these values into the formula.

$x=\frac{-(9)}{2(1)}$

Simplify this fraction.

$x=\frac{-9}{2} =-4.5$

The axis of symmetry of this quadratic function is x = -4.5.

Finding the Vertex:

Now to find the vertex, we have to take into account that this quadratic is in standard form, making it a little harder. We have to convert this function into vertex form.

Start by changing f(x) to 'y' and adding 16 to both sides.

Use the completing the square formula: $(\frac{b}{2} )^2$

$(\frac{9}{2} )^2=20.25$

Keep the balance by adding 20.25 on the left side and adding it on the right side of the equation.

Combine like terms.

Factor the right side of the equation. Ask yourself, "What two numbers multiply to 20.25 (c) and add up to 9 (b)?" These two numbers are 4.5 and 4.5. Rewrite the right side with factors.

Isolate y by subtracting 36.25 from both sides of the equation.

Now this quadratic function is in vertex form, making it super simple to find the vertex using (h, k) .

Vertex form of a quadratic is:

Compare y=(x+4.5)^2-36.25 with the original vertex form and find where h and k are. Those are the x (h) and y (k) values of the vertex.

Since the original vertex form has x - h, the h value in y=(x+4.5)^2-36.25 would be a negative since two negatives make a positive. The k value would stay "normal"---negative would mean it is a negative and positive would mean it is a positive number.

Therefore the h value is -4.5, and the k value is -36.25.

The ordered pair of the vertex is (-4.5, -36.25) .

Answer from: Quest

step-by-step explanation:

Answer from: Quest

10000

step-by-step explanation: divide by 2,

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F(x)=x^2+9x-16
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