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1 year ago

What happens if the slope is undefined? Provide an example of two points that would be on a line with an undefined slope.

Mathematics

1 answer:

AleksAgata [21]1 year ago

5 0

What happens when the slope of a line is undefined is that, the line is a vertical line that crosses the x-axis.

The points could be (1, 5) and (1, 10)

<h3>How to explain the undefined slope?</h3>

It is known that linear equations have slopes

These slopes are the average rate of change of the function

The values of these slopes can be

Zero
Positive or negative
Undefined

When the slope is undefined, it means that the line is a vertical line

An example of the vertices on such line is (x, y) and (x, y + n)

See that the x coordinate remains constant, while the y coordinate changed

Take for instance, a line that passes through (1, 5) and (1, 10) would have an undefined slope

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3 years ago

Write an equation for a parabola that has a vertex (1, 2) and passes through the point (3, -6).

Alex

Answer:

y= -2x²+4x.

Step-by-step explanation:

the common equation of the parabola is y=ax²+bx+c, where a, b, c - numbers.

1) the coordinates of the vertex are:

$x_0=-\frac{b}{2a} \ and \ y_0=\frac{4ac-b^2}{4a}.$

2) if according to the condition x₀=1, then b= -2a.

If according to the condition y₀=2, then $2=\frac{4ac-b^2}{4a}=\frac{4ac-4a^2}{4a}=c-a;$

it means that c=a+2.

3) if b= -2a; c=a+2 and the point (3;-6) belongs to the given parabola, then it is possible to substitute them into the common equation of the parabola:

-6=3²*a-6a+a+2; ⇔ a= -2.

4) if a= -2, then b=-2a=4, and c=a+2=0.

5) if a=-2, b=4 and c=0, then the required equation of the parabola is:

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