Q&A for How to Graph a Quadratic Equation

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How can you tell if a parabola will have a maximum or a minimum?

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Expert Answer

If it's positive, it's going to be upward facing. If it's negative, it's going to be downward facing. I like to remember that by saying, negative people frown and positive people smile.

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On my homework, I got x^2-x-2 and I graphed it, so how do I find the axis of symmetry?

Community Answer

Did you find the vertex when graphing it? If so, the axis of symmetry is the vertical line running through the vertex. To check your answer, it should have the equation x = 1/2.

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How do I solve a system of equations algebraically?

Donagan

Top Answerer

See the wikiHow article Solve Systems of Equations .

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Does it matter what points you plot after the vertex?

Donagan

Top Answerer

You will want to plot several points near (and on either side of) the vertex, and then not so many as you get farther from the vertex.

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I got 2(x + 1)^2 + (y - 2)^2 = 25. How will I plot it?

Donagan

Top Answerer

Solve the equation for y in terms of x (or x in terms of y). Construct a table of values for x and y. Choose convenient values for one of the variables, and calculate the corresponding values for the other variable. Plot several points and graph them. The more points you plot the more accurate the graph.

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What is the x-intercept of y = (x+2)^2 and y = 1/x?

Donagan

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The x-intercept occurs when the value of y is zero. So in the first equation, y = 0 = (x+2)², and in the second equation, y = 0 = 1/x. In each case, solve for x to find the x-intercept(s). In the first case, x = -2. That's the x-intercept. In the second case, there is no x-intercept, because when 1/x = 0, x is "undefined," meaning there is no value of x that fits into that equation. In this case, the graphed line approaches but never touches the x-axis.

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y = -x² - 4x. What are a, b and c in this format? Asked to find direction, vertex and axis.

Donagan

Top Answerer

a is -1, b is -4, and c is zero. The parabola opens downward because a is negative. The vertex is (-2,4). (The x-coordinate of the vertex is found by the expression -b / 2a, which in this case is -(-4)/(2)(-1), which equals 4 / -2, or -2. The y-coordinate of the vertex is found by substituting the x-coordinate into the original equation. Thus, the y-coordinate is -(-2)² - 4(-2) = -4 + 8 = 4.) So the vertex is (-2,4). Because the parabola open down, the axis is a vertical line passing through the vertex with the x-coordinate -2. So the axis is x= -2.

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Why is the graph of a quadratic equation not right-side or left-side parabola?

Donagan

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A quadratic equation takes the general form of either y = ax² + bx + c or x = ay² + by + c. In the second case, the parabola will open to the right side or the left side, depending on whether "a" is positive or negative.

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