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Chapter 3: Problem 76

Explain how to decide whether a parabola opens upward or downward.

Short Answer

Expert verified
To determine whether a parabola opens upwards or downwards, identify the quadratic function, then locate the leading coefficient. If the coefficient is positive, the parabola opens upwards. If the coefficient is negative, the parabola opens downwards. If the coefficient is zero, the equation does not represent a parabola.

Step by step solution

01

Identify the quadratic function

First thing to do is identifying the given quadratic function. Quadratic functions are typically in one of three forms: standard form \(y = ax^2 + bx + c\), vertex form \(y = a(x-h)^2 + k\) or factored form \(y = a(x-p)(x-q)\).
02

Identify the leading coefficient

Once the quadratic function is known, the next thing needed is to identify the leading coefficient. The leading coefficient is the coefficient of the \(x^2\) term in the standard form, the value of \(a\) in the vertex form and the factored form.
03

Determine the direction of the parabola

If the leading coefficient \(a\) is positive, then the parabola opens upward. If the leading coefficient \(a\) is negative, then the parabola opens downward. If \(a=0\), then the equation is not quadratic and does not represent a parabola.

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Most popular questions from this chapter

If you are given the equation of a rational function, explain how to find the vertical asymptotes, if there is one, of the function's graph.

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