Question

Explain why you cannot use the axes of symmetry to distinguish between the quadratic functions y=3x^2+12x+1 and y=x^2+4x+5.I'm not sure how to do this problem

Answer 1

The axes of symmetry can be used to distinguish between the two functions because they are different. The first function has a y-intercept of (0,1), while the second function has a y-intercept of (0,5).

Answer 2

Given a quadratic equation:

`y=ax^2+bx+c`

the expression to find the axis of symmetry is:

`x=-(b)/(2a)`

in this case, for the first equation, we have the following:

`\begin{gathered} y=3x^2+12x+1 \\ axis\text{ of symmetry:} \\ \Rightarrow x=-(12)/(2(3))=-(12)/(6)=-2 \\ x=-2 \end{gathered}`

for the second equation, we get:

`\begin{gathered} y=x^2+4x+5 \\ \text{axis of symmetry:} \\ \Rightarrow x=-(4)/(2(1))=-(4)/(2)=-2 \\ x=-2 \end{gathered}`

as we can see, both functions have the same axis of symmetry, that's why you cannot distinguish them. In general, several quadratic functions can have the same axis of symmetry, without being equivalent between each other.