Q&A for How to Find the Vertex of a Quadratic Equation

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What is a shortcut to find the vertex?

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Expert Answer

Average out the 2 intercepts of the parabola to figure out the x coordinate. Think of it this way—a parabola is symmetrical, U-shaped curve. So, if you have 2 x intercepts on the left and right sides of this parabola, their average will give you the x coordinate of the vertex, which is directly in the middle. Once you've figured out the x coordinate, you can plug it into the regular quadratic formula to get your y coordinate.

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How do I find x and y intercepts of a parabola?

Donagan

Top Answerer

Find the y-intercept by setting x equal to zero and solving the equation for y. Find the x-intercept by setting y equal to zero and solving for x.

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Question

How can I graph 3(x-1)squared +4 on a ti-84 calculator?

Community Answer

Press the "y=" button. Then,type in "3(x+1)^2+4)". Lastly, hit "zoom," then "0" to see the graph.

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How can you find the maximum or minimum value of a quadratic function by completing the square?

Community Answer

You wouldn't complete the square, you would factor the quadratic equation (so that it's in factored form instead of standard from).

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Question

How do I find the vertex of an equation if I know the y-intercept and two other coordinates?

Orangejews

Community Answer

You could find the standard form y=ax^2 + bx + c first. Obviously c is just the y-intercept. Two other points let you set up 2 eqs in 2 unknowns and solve for a and b. Then vertex is -b/2a per this article. There may be another short cut.

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How do you check your answer to know if it is correct?

Community Answer

You would plug in the x-coordinate into the x variables in the equation. If your answer is correct, then there would only be one y value, that is, your y-coordinate. Vertices are the only point on the graph with 1 y-value.

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Question

How do I find a smaller y value that fits in the graph?

Donagan

Top Answerer

Choose other x values that will result in smaller y values. You could also solve the equation for x and then choose whatever y values you want to use.

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Question

For the equation y = a(x-h)^2 + k, will h always be subtracted from x?

Community Answer

In the case that the "h" value is negative, it would be the subtraction of a negative number resulting in addition. Example: vertex: (1,-1), y = a(x-1)^2 + (-1) or y = a(x-1)^2 - 1. Vertex: (-1,1), y = a(x - (-1))^2 + 1 or y = a(x + 1)^2 + 1.

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Question

What is the exact formula for the y value of the vertex?

Community Answer

The formula for y-coordinate of the vertex (k): (h)^2 + b(h) + c = k (h = x-coordinate of vertex, k = y-coordinate of the vertex).

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How can I catch my errors when completing the square?

Community Answer

Go back and check your work. Ask youself if your answer makes sense.

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Question

When will this ever have use in my life? If not, then why am I studying it?

Donagan

Top Answerer

You're studying it because you don't know for certain which specific knowledge you'll need in your future life. Quadratic equations are used often in engineering and design work.

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Question

How do I find the zeros?

Community Answer

You can find the zeroes by alpha + beta = -b/a , alpha*beta = c/a , alpha - beta = b^2-4ac/|a|.

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