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Chapter 2: Problem 79

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

Short Answer

Expert verified
A parabola, defined by the quadratic function \( f(x) = ax^2 + bx + c \), opens upwards when the coefficient 'a' is greater than 0 and downwards when 'a' is less than 0.

Step by step solution

01

Identify the Quadratic Form

Any quadratic function can be written in the form \( f(x) = ax^2 + bx + c \) where \( a \), \( b \), and \( c \) are constants and \( a \) is not equal to zero. Identify the quadratic equation you are dealing with and get it in this form, so you can easily see the coefficients.
02

Notice the Coefficient 'a'

In a quadratic function, the coefficient 'a' (which is the number in front of the \( x^2 \)) determines the direction of the parabola. It is the leading coefficient.
03

Decipher the Direction of Opening

If the coefficient 'a' is greater than 0, the parabola opens upwards. If 'a' is less than 0, the parabola opens downwards.

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