Math  /  Algebra

QuestionFill in the information about the parabolas below. (a) For each parabola, choose whether it opens upward or downward. y=x2: (Choose one) vy=13x2: (Choose one) vy=12x2: (Choose one) v (Choose one) vy=-x^{2}: \text { (Choose one) } v y=-\frac{1}{3} x^{2}: \text { (Choose one) } v \quad y=\frac{1}{2} x^{2}: \text { (Choose one) } v \text { (Choose one) } v (b) Choose the parabola with the narrowest graph. y=x2y=-x^{2} y=13x2y=-\frac{1}{3} x^{2} y=12x2y=\frac{1}{2} x^{2} y=3x2y=-3 x^{2} (c) Choose the parabola with the widest graph. y=x2y=-x^{2} y=13x2y=-\frac{1}{3} x^{2} y=12x2y=\frac{1}{2} x^{2} y=3x2y=-3 x^{2}

Studdy Solution
Identify the parabola with the widest graph by comparing the absolute values of the coefficients a a .
The parabola with the smallest a|a| is y=13x2 y = -\frac{1}{3}x^2 , so it has the widest graph.
(a) Directions: - y=x2 y = -x^2 : downward - y=13x2 y = -\frac{1}{3}x^2 : downward - y=12x2 y = \frac{1}{2}x^2 : upward
(b) Narrowest graph: y=3x2 y = -3x^2
(c) Widest graph: y=13x2 y = -\frac{1}{3}x^2

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