Solve the quation.
1 answer:
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Answer:
Step-by-step explanation:
I believe you meant y = 2(x − 4)^2 + 5. Use the symbol ' ^ " to indicate exponentiation. This equation has the vertex form of the equation of a quadratic. The x-coordinate of the vertex is 4 and the y-coordinate is 5. Thus, the vertex is at (4, 5). The multiplier 2 stretches the graph vertically by a factor of 2.
To aid us in graphing this function, find the x- and y-intercepts:
If x = 0, y = 2(-4)^2 + 5, or 37. Therefore the y-intercept is at (0, 37).
If y = 0, then
2(x − 4)^2 + 5 = 0,
2(x − 4)^2 = -5 But a square cannot be negative, so there is no x-intercept in this case.
To graph this function, plot the vertex (4, 5) and the y-intercept (0, 37). Take advantage of symmetry and find another point across x = 4 from (0, 37): It is (8, 37).
Answer:
The coordinate pair of the point D that will make AB perpendicular to CD is the D(6, 3)
Step-by-step explanation:
The slope of the given line AB can be presented as follows;
The slope of a perpendicular line to a given line is equal to the negative reciprocal of the slope of the given line
Therefore, the slope of the perpendicular to a line that has a slope of m is -1/m
The slope of the perpendicular to the line AB is therefore
From which we get the equation of the perpendicular to the line AB given as follows;
y - 4 = -1/3 × (x - 3)
y - 4 = -x/3 + 1
y = -x/3 + 1 + 4
y = -x/3 + 5
When x = 6, y = -6/3 + 5 = 3
Therefore, the coordinate pair of the point D that will make AB perpendicular to CD is the D(6, 3).