Parabolas: find line of symm. for y = -2(x + 4)^2 + 6

[askmemath]

Identify the vertex of the parabola defined by y = 2x2 + 8x + 9.

Identify the line of symmetry of the parabola defined by y = –2(x + 4)2 + 6.

Thank you.

 

[jonboy]

Identify the vertex of the parabola defined by \(\displaystyle \L \;y\,=\,2x^2\,+\,8x\,+\,9\).

Given a quadratic in the form: $\displaystyle ax^2\,+\,bx\,+\,c$

The vertex is: \(\displaystyle \L \;(\frac{\,-\,b}{2a}\,,\,f(\frac{\,-\,b}{2a}))\)

So we find b and a to get the x coordinate of the vertex:

\(\displaystyle \L \;\frac{\,-\,b}{2a}\,=\,\frac{\,-\,8}{2(2)}\,=\,-\,2\)

The we plug that back in to get the y coordinate of the vertex.

So solve: $\displaystyle y\,=\,2(\,-\,2)^2\,+\,8(\,-\,2)\,+\,9$

To get an answer $\displaystyle (\,-\,2\,,\,y)$

For the second, find the x coordinate of the vertex and put x = that and you'll have the line of symmetry.

 

[tkhunny]

Re: Parabolas

Identify the line of symmetry of the parabola defined by y = –2(x + 4)^2 + 6.

Line of Symmetry is staring at you.

y = –2(x + 4)^2 + 6

x + 4 = 0 ==> x = -4

This is an eyeball problem. Never use paper for one of these again.

 

[jonboy]

Line of Symmetry is staring at you.

Ahh yeah.

It's in the form: \(\displaystyle \L \;y\,=\,a(x\,-\,h)^2\,+\,k\)

In which h it the x - intercept of the vertex.

We can change + 4 to - (-4) to get it in that form.

So we have: \(\displaystyle \L \;y\,=\,2(x\,-\,(\,-\,4))^2\,+\,6\)

Thus the axis of symmetry is x = -4.

 

[tkhunny]

x - intercept of the vertex.
Thus the vertex is x = -4.

I'm sure you mean "Line of Symmetry". The vertex is a point.

 

[jonboy]

x - intercept of the vertex.
Thus the vertex is x = -4.

I'm sure you mean "Line of Symmetry". The vertex is a point.

Yeah lol thanks for pointing that out.