The equation of a parabola is given in factored form.

Mathematics

1 answer:

ValentinkaMS [17]3 years ago

7 0

Answer:

The parabola's axis of symmetry is x = -6

Step-by-step explanation:

Parabola general equation:

y = a*(x - r1)*(x - r2)

Equation given:

y = (-1/4)*(x + 2)*(x + 10)

a = -1/4

r1 = -2

r2 = -10

To check if the parabola passes through the point (2, 10) it is necessary to replace x = 2 and check the y-value, as follows:

y = (-1/4)*(2+ 2)*(2 + 10) = -12

Then, point (2, 10) is not included in the parabola.

If a > 0 then the parabola opens upward; if a < 0 then the parabola opens downward. Then, the parabola opens downward

Axis of symmetry:

h = (r1 + r2)/2

h = (-2 + -10)/2 = -6

Then, The parabola's axis of symmetry is x = -6

To find Parabola's vertex, replace with the axis of symmetry:

y = (-1/4)*(-6 + 2)*(-6 + 10) = 4

Therefore, the parabola has a vertex at (-6, 4)

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If line a is perpendicular to line b and the slope of line a is 7 whats the slope of line b

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Answer:

If a line is perpendicular to another line, that means that the slope is completely opposite that of the original line. The first thing that we do to the slope is we negate the number which means that if we have a slope of $-7$ our slope because $7$ in this step. In our case our slope is $7$ so in this step it becomes $-7$ .

Moving onto the second part which is to get the reciprocal of the number which means that if we have $\frac{1}{2}$ then we would switch it to $2$ . In our case our number is $-7$ so we would make that into a fraction like this $-\frac{1}{7}$ .