Q71. - Algebra 1

Question

REASONING The graph of a quadratic function has a vertex at $\left(2,0\right)$. One point on the graph is $\left(5,9\right)$. Find another point on the graph. Explain how you find it.

Step-by-Step Solution

Answer

Another point on the graph is $\left(-\mathbf{1}\mathbf{,}\mathbf{9}\right)$.

Step 1. Define Vertex.

The axis of symmetry intersects a parabola at only one point is called vertex.

Step 2. Graph.

The vertex of the graph of the quadratic function is at $\left(2,0\right)$ and one point on the graph is $\left(5,9\right)$. Graph these two points.

Step 3. Explanation.

From the graph, it can be observed that the axis of symmetry cuts the parabola into two equal halves. 

First count the spaces over and up from the vertex to the point $\left(5,9\right)$ and do the same on the opposite side. By doing this we get another point on the graph, that is, point $\left(-1,9\right)$.

 

Therefore, another point on the graph is $\left(-1,9\right)$.