How do you find the vertex of a parabola on a graphing calculator?

Type the function beginning with y =, then tap the curve. The turning point is marked with both coordinates. The first is the input at which the function turns, and the second is its greatest or least value.

Does the question want the x-value or the y-value of the vertex?

Read the last sentence of the question. When, where, at what price or how many hours asks for the input, the x-value. Greatest, least, maximum height or maximum profit asks for the output, the y-value. Both numbers are usually among the answer choices.

When is it faster not to graph it?

When the function is already written as a(x - h)^2 + k. The turning point is (h, k), and reading it off the equation is quicker than typing it in.

I graphed it and cannot see the curve turn. Why?

The turning point is outside the window. A model whose values run into the hundreds needs a much taller window than the one the calculator opens with, so zoom out or drag upwards until the curve bends.

Find the maximum or minimum of a quadratic by graphing it

Graph the quadratic and tap the curve. The turning point is marked with both coordinates: the input, and the greatest or least value.

1.Type the function as printed, with $x$ as the input even if the question calls it $t$ . Begin with $y =$ so that it graphs.
2.Zoom out until you can see the curve turn. A model with values in the hundreds needs a tall window.
3.Tap the curve. The turning point is marked $(x, y)$ .
4.Decide which half the question wants. The $x$ -value is when or where it happens; the $y$ -value is the greatest or least amount.

Try it on a question

Work it below before you open the working. The steps say what to do, and you can do each one yourself.

A stall's daily profit, in dollars, when it prices a jar of honey at $x$ dollars is modelled by $P(x) = -4x^2 + 56x - 96$ . What is the greatest daily profit the model predicts?

Choice A: $7$
Choice B: $96$
Choice C: $100$
Choice D: $492$

1
Type the model with $x$ as the price, and begin with $y =$ so that it graphs. The window is already tall enough to show the turn.
Type: y = -4x^2 + 56x - 96
2
Find the answer on the graph. Tap a line or a curve to mark its points.

Open in the full calculator

Loading the calculator…

The full working, and why each wrong choice is there

By hand: the turning point is at $x = -\frac{56}{2(-4)} = 7$ , and $P(7) = -4(49) + 56(7) - 96 = -196 + 392 - 96 = 100$ .

In the calculator: type $y = -4x^2 + 56x - 96$ and tap the curve. It turns at $(7, 100)$ . The question asks for the profit, which is the $y$ -value: 100. The 7 is the price that gives it, and it is an answer choice for exactly that reason.

Choice A: $7$
This is the price that gives the greatest profit: the $x$ -value of the turning point. The question asks for the profit.
Choice B: $96$
This is the constant in the model with its sign dropped. It is not a value the profit reaches at the turning point.
Choice C: $100$ the answer
The curve turns at $(7, 100)$ , and the profit is the $y$ -value.
Choice D: $492$
This comes from adding $4 \times 49$ where the model subtracts it. The squared term is negative.

Use it when

A quadratic model, and the question asks for the maximum, the minimum, or the input at which it happens.
The quadratic is in standard form $ax^2 + bx + c$ , where the turning point is not visible in the equation.
The coefficients are decimals or large numbers, where $-\frac{b}{2a}$ invites an arithmetic slip.

Do not use it when

The function is already in vertex form $a(x - h)^2 + k$ . The turning point is $(h, k)$ , read straight off the equation.
The question asks which equation shows the maximum or minimum as a constant. That is a question about form, and the choices are equations.
A coefficient is a letter. The calculator needs a number for it before it can draw anything.

Five questions on this move

Untimed, and nothing is saved. A wrong first answer gets one more try before the working is shown.

Question 1 of 5

$f(x) = 2x^2 - 12x + 11$

What is the minimum value of the given function?

Five is a start

In your account there is a focused set of ten on Nonlinear functions from the question bank, with the same one more try. And after each practice test, the drills your plan sets for the skills you missed name the moves for them.

Practise Nonlinear functions in your account

How this page was checked

Every maths answer, by our own calculator
The answer to each of the 6 questions on this page is worked out again by our calculator engine in an automated test, which fails when a key disagrees with the engine.
In the calculator the test uses
Claude (an AI assistant) typed this page's calculator steps into the College Board version of the Desmos calculator on 14 October 2026 and read the same answers. All six parabolas on this page were typed in exactly as printed, and each turning point was the keyed one.
The whole page, by a person
Not yet. Every question and every step of its walk-through was worked through in a browser by Claude, an AI assistant, on 14 October 2026. The page was published on 14 October 2026 before a person had read it. If something here is wrong, tell us and it is put right.

The questions were drafted with AI and are original: none is a College Board question, and none comes from the question bank behind our practice tests.

Where this comes from

“Tap the turning point” is one card from the Preptics lesson Quadratic models: the vertex input, then the vertex value, which sits under the Digital SAT skill Nonlinear functions. The lesson has the other cards around it, and its questions come back for review on a schedule. The lessons are part of the Digital SAT track.

Common questions

How do you find the vertex of a parabola on a graphing calculator?: Type the function beginning with y =, then tap the curve. The turning point is marked with both coordinates. The first is the input at which the function turns, and the second is its greatest or least value.
Does the question want the x-value or the y-value of the vertex?: Read the last sentence of the question. When, where, at what price or how many hours asks for the input, the x-value. Greatest, least, maximum height or maximum profit asks for the output, the y-value. Both numbers are usually among the answer choices.
When is it faster not to graph it?: When the function is already written as a(x - h)^2 + k. The turning point is (h, k), and reading it off the equation is quicker than typing it in.
I graphed it and cannot see the curve turn. Why?: The turning point is outside the window. A model whose values run into the hundreds needs a much taller window than the one the calculator opens with, so zoom out or drag upwards until the curve bends.

Keep going

Every move: the full set. The calculator on its own: the graphing calculator.

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