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Given:
The graph of a quadratic function passes through the points (5,31) (3,11) (0,11).
To find:
The equation of the quadratic function.
Solution:
A quadratic function is defined as:
...(i)
It is passes through the point (0,11). So, substitute in (i).
Putting in (i), we get
...(ii)
The quadratic function passes through the point (5,31). So, substitute in (ii).
Divide both sides by 5.
...(iii)
The quadratic function passes through the point (3,11). So, substitute in (ii).
Divide both sides by 3.
...(iv)
Subtracting (iv) from (iii), we get
Putting in (iv), we get
Putting in (ii), we get
Therefore, the required quadratic equation is .
Answer:
The y-intercept of the line that passes through the point (3, -6) and which has a slope of 4 is -18.
Step-by-step explanation:
We represent the straight line by using this formula from Analytical Geometry:
Where:
- Independent variable, dimensionless.
- Dependent variable, dimensionless.
- Slope, dimensionless.
- y-Intercept, dimensionless.
Now we clear the y-intercept:
If we know that ,
and
, the y-intercept of the line is:
The y-intercept of the line that passes through the point (3, -6) and which has a slope of 4 is -18.