What is the axis of symmetry for f(x) = −2×2 + 20x − 42?

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Mina Herzog · Accepted Answer

For a general equation y = ax^2 + bx + c We need to convert it to vertex form which includes complete factoring.y = a[ x^2 + (b/a)x + c/a ]Now examining x^2 + (b/a)x + c/aIf you look at square of bionomial (z + u)^2 = z^2 + 2zu + u^2, and compare it with what we have, you will see the “u” term had to have been b/(2a) so when it’s multiplied by 2z = 2x, you get (b/a)x.Hence to satisfy the perfect square we must have (b / (2a))^2 = b^2 / (4a^2), but then when we add it we must also subtract it.x^2 + (b/a)x + b^2/(4a^2) – b^2/(4a^2) + c/aNow the first 3 terms factor and the other stuff hangs out front.(x + b/(2a))^2 – b^2/(4a^2) + c/a And now finally returning toy = a[ (x + b/(2a))^2 – b^2/(4a^2) + c/a ]y = a[x + b/(2a)]^2 – b^2/(4a)+cSo suppose a is positive, then the parabola will open up. Where is the expression of lowest value? Obviously when x + b/(2a) = 0, meaning x = -b / (2a) which is where the vertex is and that is the axis of symmetry.So now you can find the axis of symmetry of any parabola of the given form by just doing -0.5b/a.

Mina Herzog · Answer

You have some notation problems, but it looks like you are trying to define a quadratic function in expanded form: f(x) = ax² + bx + cIn that case, the graph of the equation y = f(x) has this axis of symmetry:x = -b/(2a)

Lavinia Carroll

What is the axis of symmetry for f(x) = −2×2 + 20x − 42?

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