The graph of the quadratic function is shown.
Which choice gives the value of ?
For a function given by a graph, treat as a reading question: go directly to on the graph (the -axis) and read the corresponding -value. This avoids unnecessary algebra and is usually the fastest approach.
Hints
Connect to the graph
Find the point on the graph where .
Look at the -axis
When , you are on the -axis. Read the -value where the curve meets that axis.
Read the coordinate carefully
Use the tick marks to make sure you read the correct integer value.
Desmos Guide
Enter points seen on the graph
In Desmos, create a table and enter three clear points from the graph, such as , , and .
Fit a quadratic model
Type y1 ~ a x1^2 + b x1 + c to perform a quadratic regression based on the table.
Evaluate at
Use the regression equation Desmos gives to find the output when (substitute into the model) to obtain .
Step-by-step Explanation
Identify what means
Since is the output when , it is the -coordinate of the point on the graph where (the -intercept).
Read the value from the graph
On the graph, when , the parabola passes through the point . Therefore, the value of the function at is .