Q&A for How to Find an Axis of Symmetry

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What is the axis of symmetry of f for f(x)=-2|x+3|-7?

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The axis of symmetry is x=-3, because the vertex is at (-3,7). It is an absolute value graph that faces down.

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What is the axis of symmetry in x = -2(x - 3) + 5?

Donagan

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Because this graph consists of a straight line, it does not have an axis of symmetry. Axes of symmetry occur with parabolic graphs representing quadratic equations ("second-degree" polynomials).

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What is the axis of symmetry of f(x) = -x^2 - 6x + 4?

Donagan

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As explained in the above article, the axis of symmetry of a second-degree polynomial in the form of ax² + bx + c is given by the formula x = -b/2a, which in this case is x = -(-6) / 2(1) = 6/2 = 3. x=3.

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How do I find the vertex?

Donagan

Top Answerer

See Find the Vertex .

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How do you find the axis of symmetry for a hyperbola?

Community Answer

A hyperbola has two axes of symmetry. One of them is the line passing through both foci. The other is the perpendicular bisector of the foci.

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How do I find a quadratic equation given 2 points and a maximum (max y coordinate)?

Community Answer

Use the vertex form for the quadratic function: y = a(x-h)^2 + k. The value of k is the y-coordinate of the vertex which was given to you as the max, so substitute that in first. Then use the other two (x,y) pairs to get two equations in two unknowns, a and h. You can solve the system by solving one equation for a and substituting into the other. But since the equations are quadratic in h, you won't get a unique solution. One solution corresponds to a steep parabola with vertex between the other two given points; the other is a shallow parabola with a vertex is further out.

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