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klemol [59]
3 years ago
7

Which of the quadratic functions has the narrowest graph?

Mathematics
1 answer:
topjm [15]3 years ago
6 0

A quadratic function's graph being wide or narrow is determined or depended on a-term:

\large{y = a {x}^{2}  + bx + c}

If |a| has a lot of value, for example a = 2 or a = 100. The graph will get narrower if increasing the value of |a|. On the other hand, If |a| has small value, for example a = 1/2 or a = 1/10000. The graph would be wide.

Also it does not matter if a-term is negative or not since a-term being positive or negative determines if a parabola is upward or downward. Only |a| determines how narrow/wide the graph is.

From the question, it is clear that the parabola y = 2x^2 is the narrowest graph since it has the highest |a| value out of all choices.

Answer

  • y = 2x^2
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Step-by-step explanation:

3 inches= 50 miles

1 inch = 50/3 miles

7 inches = 50/3 × 7 miles

= 116.66666667 miles

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3 years ago
What are the x- and y- coordinates of point E, which partitions the directed line segment from A to B into a ratio of 1:2?
Solnce55 [7]

<u><em>The coordinates of the points A and B are not given. We'll assume: A(3,1) B(12,-5)</em></u>

Answer:

<em>The coordinates of E are (6,-1)</em>

Step-by-step explanation:

<u>Partition of a Segment</u>

The length of segment directed from A(xa,ya) to B(xb,yb) can be decomposed in its x,y coordinates:

x_{AB}=x_b-x_a

y_{AB}=y_b-y_a

If a point E is to be in the segment and partition it into a ratio 1:2, then

\displaystyle \frac{x_{AE}}{{x_{EB}}=\frac{y_{AE}}{{y_{EB}}=\frac{1}{2}

But

x_{AE}=x_e-x_a

y_{AE}=y_e-y_a

x_{EB}=x_b-x_e

y_{EB}=y_b-y_e

Then we set the equation:

\frac{x_{AE}}{{x_{EB}}=\frac{1}{2}

2(x_e-x_a)=x_b-x_e

Operating and rearranging

3x_e=x_b+2x_a

Solving

\displaystyle x_e=\frac{x_b+2x_a}{3}=\frac{12+6}{3}

x_e=6

Similarily

\displaystyle y_e=\frac{y_b+2y_a}{3}=\frac{-5+2}{3}

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The coordinates of E are (6,-1)

8 0
4 years ago
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Step-by-step explanation:

Given

2y - 2x = -8 -- correct expression

Required

Represent as slope intercept form

2y - 2x = -8

Make 2y the subject

2y = 2x - 8

Divide through by 2

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Answer:

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Erica paid ...

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3 years ago
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