Q8. - Algebra 1

Question

Record your answers on the answer sheet provided by your teacher or on a sheet of paper.

Use the graph of the quadratic equation shown below to answer each question.

 

A What is the vertex?

B What is the $y$-intercept?

C What is the axis of symmetry?

D What are the roots of the corresponding quadratic equation?

Step-by-Step Solution

Answer

A The vertex is $\left(1,4\right)$.

B The $y$-intercept is 3.

C  The axis of symmetry is $x=1$.

D The roots of the corresponding quadratic equation are $-1$ and 3.

Part a. Step 1. Observe the graph.

The graph is:

Part a. Step 2. Find the vertex.

From the above graph, it can be noticed that the vertex is $\left(1,4\right)$.

Part b. Step 1. Observe the graph.

The graph is:

Part b. Step 2. Find the -intercept.

From the above graph, it can be noticed that the $y$-intercept is 3.

Part c. Step 1. Observe the graph.

The graph is:

 

Part c. Step 2. Find the axis of symmetry .

From the above graph, it can be noticed that the axis of symmetry is $x=1$.

Part d. Step 1. Observe the graph.

The graph is:

Part d. Step 2. Find the roots of the corresponding quadratic equation.

From the above graph, it can be noticed that the roots of the corresponding equation are $-1$ and 3.