Questions: MATH-1215Y-001 Fall 2024 Quadratic Equations and Functions How the leading coefficient affects the shape of a parabola Fill in the information about the parabolas below. (a) For each parabola, choose whether it opens upward or downward. y=1/4 x^2: upward y=1/3 x^2: upward

MATH-1215Y-001 Fall 2024
Quadratic Equations and Functions
How the leading coefficient affects the shape of a parabola

Fill in the information about the parabolas below.
(a) For each parabola, choose whether it opens upward or downward. y=1/4 x^2: upward y=1/3 x^2: upward

Transcript text: MATH-1215Y-001 Fall 2024 Quadratic Equations and Functions How the leading coefficient affects the shape of a parabola Fill in the information about the parabolas below. (a) For each parabola, choose whether it opens upward or downward. $y=\frac{1}{4} x^{2}:$ upward $y=\frac{1}{3} x^{2}:$ upward

Solution

Solution Steps

Step 1: Determine the Opening Direction

The sign of the leading coefficient $a = 0.25$ determines the parabola's opening direction. Since $a = 0.25$, the parabola opens upward.

Step 2: Determine the Width of the Parabola

The absolute value of the leading coefficient $|a| = 0.25$ affects the width of the parabola. A larger $|a|$ results in a narrower graph, while a smaller $|a|$ results in a wider graph. Given $|a| = 0.25$, the parabola is considered wider.

Final Answer:

The parabola described by $y = 0.25x^2 + 0x + 0$ opens upward and is wider compared to a parabola with $|a| = 1$.

Step 1: Determine the Opening Direction

The sign of the leading coefficient $a = 0.333$ determines the parabola's opening direction. Since $a = 0.333$, the parabola opens upward.

Step 2: Determine the Width of the Parabola

The absolute value of the leading coefficient $|a| = 0.333$ affects the width of the parabola. A larger $|a|$ results in a narrower graph, while a smaller $|a|$ results in a wider graph. Given $|a| = 0.33$, the parabola is considered wider.

Final Answer:

The parabola described by $y = 0.3333333333333333x^2 + 0x + 0$ opens upward and is wider compared to a parabola with $|a| = 1$.

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