Are these two phrases the sameI am not sure what it is asking for.

[squirt552]

Homework Statement

First example f(x)=1/4 (x+4)^2 +7
Asks for vertex and the line of symmetry and the value of f(x) and maximim or minimum
This is no problem vertex= (-4,7) line of symmetry is -4 value f(x)= 7


second problem f(x)=x^2 -10x -2

vertex (5, -27)
but now ask for the equation of the line of symmetry


Is: the line of symmetry and: the equation of the line of symmetry the same thing?

information shows the line of symmetry is x= - b/2a. okay so how do I show this as an equation if the line of symmetry is 5

Homework Equations

The Attempt at a Solution

 

[tiny-tim]

Welcome to PF!

Hi squirt552! Welcome to PF!

line of symmetry is -4 …

hmm … line of symmetry is x = -4

Is: the line of symmetry and: the equation of the line of symmetry the same thing?

Well, you have to describe the line in some way, and the easiest (and only sensible) way is by using an equation, so … yes!

information shows the line of symmetry is x= - b/2a. okay so how do I show this as an equation if the line of symmetry is 5

(you mean x = 5)

Well, if the line of symmetry is x= - b/2a and x = 5,

then that means that - b/2a = … ?

 

[Blueshift5]

No, the phrase "line of symmetry" and "equation of the line of symmetry" are not the same thing. The line of symmetry is the vertical line that divides the parabola into two equal halves, and the equation of the line of symmetry is the equation of that line. In the second problem, the line of symmetry is x=5, and the equation of the line of symmetry would be x=5. In general, the equation of the line of symmetry for a parabola with the equation f(x)=ax^2+bx+c is x=-b/2a. So for the given problem, the equation of the line of symmetry would be x=-(-10)/2(1), which simplifies to x=5.