Question

1. what is the range of the quadratic function graphed below?

options:
a. $y \geq 1$
b. $x \geq 1$
c. all real numbers
d. $y \leq 1$

Explanation:

Step1: Identify the vertex and direction

The graph is a parabola opening upwards (since it's a U - shape opening up), so the vertex is the minimum point. From the graph, the vertex is at (0, 1), so the minimum value of \(y\) is 1.

Step2: Determine the range

The range of a function is the set of all possible \(y\) - values. For a parabola opening upwards with vertex at \(y = 1\), the \(y\) - values start from 1 and go to positive infinity. So the range is \(y\geq1\).

Step3: Eliminate incorrect options

• Option B: The range is about \(y\) - values, not \(x\) - values, so B is incorrect.
• Option C: The parabola has a minimum value, so it doesn't include all real numbers, C is incorrect.
• Option D: The parabola opens upwards, so \(y\) is greater than or equal to 1, not less than or equal to 1, D is incorrect.

Answer:

A. \(y\geq1\)