How do you find the y coordinate of the vertex of a parabola?

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Answer 1 · 2018-07-07T06:11:41

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Given: a parabola equation

If the parabola equation is in the form: $f(x) = Ax^2 + Bx + C = 0$

The vertex is $(-B/(2A), f(-B/(2A)))$

Once you have the $x$ value of the vertex, just evaluate the function with that $x$ -value.

Example: $f(x) = 3x^2 -2x - 9$

$x = -(-2)/(2*3) = 2/6 = 1/3$

$f(1/3) = 3 (1/3)^2 - 2/1 * 1/3 - 9$

$f(1/3) = 3/1 * 1/9 - 2/3 - 9$

$f(1/3) = 3/9 - 2/3 - 9$

$f(1/3) = 1/3 - 2/3 - 9/1 * 3/3$

$f(1/3) = -1/3 - 27/3 = -28/3 = -9 1/3$

vertex: $(1/3, -28/3)$