How do you find the vertex from standard form?

Compute x = −b/(2a), then substitute that x back into the equation for y. The vertex is that (x, y) point.

When is the vertex a maximum vs a minimum?

Look at a: if a is positive the parabola opens up and the vertex is a minimum; if a is negative it opens down and the vertex is a maximum.

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How is this different from IXL?

No punishing score. A wrong answer gives you a step-by-step explanation, not a number that drops — and every question is reviewed by a human before you see it.

Algebra 2 practice

Finding the Vertex of a Parabola — Practice

Find the turning point of any parabola — from standard form with $x = -\frac{b}{2a}$ , or by reading vertex form directly — with every step explained.

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What you'll practice

The vertex is a parabola's maximum or minimum point, and everything about graphing quadratics hangs off it. From standard form $y = ax^2 + bx + c$ , the x-coordinate is $x = -\frac{b}{2a}$ ; substitute back for y. From vertex form $y = a(x-h)^2 + k$ , the vertex $(h, k)$ can be read directly — signs permitting. These questions cover both, plus max/min interpretation.

Worked example

Find the vertex of $y = x^2 - 6x + 5$ .

x-coordinate: $x = -\frac{b}{2a} = -\frac{-6}{2(1)} = 3$ .
Substitute back: $y = (3)^2 - 6(3) + 5 = 9 - 18 + 5 = -4$ .
Vertex: $(3, -4)$ .
Since $a = 1 > 0$ , the parabola opens upward — the vertex is a minimum.

Common mistakes

Sign error in $-\frac{b}{2a}$ : with $b = -6$ , the x-coordinate is $+3$ , not $-3$ .
Reading vertex form with the wrong sign: $y = (x-1)^2 + 7$ has vertex $(1, 7)$ , not $(-1, 7)$ — the form is $(x - h)$ .
Stopping after x: the vertex is a point. Substitute back to get the y-coordinate.

Try a few

1. Find the vertex of $y = x^2 + 4x + 1$ .

$(-2, -3)$
$(2, 13)$
$(-2, 1)$
$(-4, 1)$

2. Find the vertex of $y = 2x^2 - 8x + 3$ .

$(2, -5)$
$(-2, 27)$
$(2, 3)$
$(4, 3)$

3. What is the maximum value of $y = -(x-1)^2 + 7$ ?

$7$ , at $x = 1$
$7$ , at $x = -1$
$1$ , at $x = 7$
It has no maximum

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FAQ

How do you find the vertex from standard form?: Compute x = −b/(2a), then substitute that x back into the equation for y. The vertex is that (x, y) point.
When is the vertex a maximum vs a minimum?: Look at a: if a is positive the parabola opens up and the vertex is a minimum; if a is negative it opens down and the vertex is a maximum.
Is Cramzoo free?: Cramzoo is free to start — every unit opens with free skills and no account is needed. This particular skill is part of Premium ($6/month or $30/year), which unlocks every skill plus the parent progress dashboard.
How is this different from IXL?: No punishing score. A wrong answer gives you a step-by-step explanation, not a number that drops — and every question is reviewed by a human before you see it.

Related Algebra 2 skills

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