That is because there are many quadratic functions that have the same axis of symmetry. If a function is multiplied by a constant factor the axis of symmetry remains the same but the curved part of the graph widens or narrows.
For example x^2 + x - 6 and 2x^2 + 2x - 12 The last function will have same axis of symmetry and same roots as the first but the curved part will be narrower.
Also if we multiply the first function by -1 the curve will flip about the x axis but will have the same axis of symmetry
We cannot use the axes of symmetry to distinguish between the quadratic functions because the quadratic functions may have same line of symmetry but different characteristics.
The axis of symmetry is an imaginary straight line that divides any graph or figure into two identical parts.
The standard form of the quadratic functions is [tex]y = ax^2 + bx + c,[/tex] where a, b, and c are real numbers. And all the quadratic functions are parabola that opens up or opens down.
All the quadratic functions have a line of symmetry and the quadratic functions may have the same line of symmetry. That is [tex]x^2 + 2x - 8[/tex] and [tex]3x^2 + 6x - 24[/tex] have the same axis of symmetry and same roots.
The graph is [tex]x^2 + 2x - 8[/tex] narrower than[tex]3x^2 + 6x - 24[/tex] but they both have the same line of symmetry.
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