How to determine the direction a parabola opens
1 answer:
Answer:
Upward or Downward
Step-by-step explanation:
A parabola is the graph of a quadratic function y = ax2 + bx + c. The graphs below depict two typical parabolas:
For clarity, we indicate their x-intercepts with red dots, their y-intercepts with pink dots, and the vertex of each parabola with a green dot:
The first parabola (a U shape) opens vertically, whereas the second parabola opens downwards (is an upside down U shape).
Given the function y = ax2 + bx + c, write the following:
- <em>If an is greater than zero (positive), the parabola widens upward.</em>
- <em>If the value is 0 (negative), the parabola expands downward.</em>
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Answer:
The equation of the line that passes through the points (0, 3) and (5, -3) is .
Step-by-step explanation:
From Analytical Geometry we must remember that a line can be formed after knowing two distinct points on Cartesian plane. The equation of the line is described below:
(Eq. 1)
Where:
- Independent variable, dimensionless.
- Dependent variable, dimensionless.
- Slope, dimensionless.
- y-Intercept, dimensionless.
If we know that and
, the following system of linear equations is constructed:
(Eq. 2)
(Eq. 3)
The solution of the system is: ,
. Hence, we get that equation of the line that passes through the points (0, 3) and (5, -3) is
.