Question

F(x)=x^2+9x-16 What is vertex Axis of semetry

Answer 1

Answer:

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 $x$ 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 2

Answer:

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: 1
• b: 9
• c: -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.

• $y+16=x^2+9x$

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.

• $y+16+20.25=x^2+9x+20.25$

Combine like terms.

• $y+36.25=x^2+9x+20.25$

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.

• $y+36.25=(x+4.5)(x+4.5)$
• $y+36.25=(x+4.5)^2$

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

• $y=(x+4.5)^2-36.25$

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:

• $y=a(x-h)^2+k$

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 $(-4.5, -36.25)$.