Section 6.3 Graphing Parabolas
Subsection 1. Find the coordinates of points on a parabola
To find the \(x\)-coordinate of a point on a parabola, we usually need to solve a quadratic equation.
Subsubsection Examples
Example 6.39.
Find the \(y\)-coordinate of the point on the graph of \(~y=2x^2-3x+5~\) with \(x\)-coordinate \(-3\text{.}\)
Substitute \(x=\alert{-3}\) into the equation, and evaluate.
The \(y\)-coordinate is 32, and the point is \((-3,32)\text{.}\)
Example 6.40.
Find the \(x\)-coordinates of all points on the graph of \(~y=20-3x^2~\) with \(y\)-coordinate \(-28\text{.}\)
Substitute \(y=\alert{-28}\) into the equation, and solve.
The points are \((4, -28)\) and \((-4,-28)\text{.}\)
Subsubsection Exercises
Checkpoint 6.41.
Find the \(y\)-coordinate of the point on the graph of \(~y=-x^2+6x+2~\) with \(x\)-coordinate \(-2\text{.}\)
Checkpoint 6.42.
The \(x\)-coordinate of the vertex of \(~y=2x^2-6x+1~\) is \(\dfrac{3}{2}\text{.}\) Find the \(y\)-coordinate of the vertex.
Checkpoint 6.43.
Find the \(x\)-coordinates of all points on the graph of \(~y=x^2-2x+5~\) with \(y\)-coordinate 8.
Checkpoint 6.44.
Find the \(x\)-intercepts of the graph of \(~y=\dfrac{1}{4}x^2-5x+24~\text{.}\)
Subsection 2. Find the average of two numbers
The average of two numbers lies half-way between them on a number line. To find their average, we take one-half of their sum. That is, the average of \(p\) and \(q\) is
Subsubsection Example
Example 6.45.
The average of 4 and 9 is
Example 6.46.
The average of \(-8\) and \(4\) is
Example 6.47.
The average of \(\dfrac{5}{2}\) and \(\dfrac{-3}{4}\) is
Subsubsection Exercises
Checkpoint 6.48.
Find the average of \(-12\) and \(-7\text{.}\)
Checkpoint 6.49.
Find the average of \(-4\) and \(\dfrac{1}{2}\text{.}\)
Checkpoint 6.50.
Find the average of \(\dfrac{3}{2}\) and \(\dfrac{9}{2}\text{.}\)
Checkpoint 6.51.
Find the average of \(\dfrac{9}{4}\) and \(\dfrac{-3}{4}\text{.}\)