Question

I need help finding the domain and range!! -Algebra

Answer 1

Answer:

• The graph is shown below
• Vertex = (2,1)
• Axis of symmetry is x = 2
• Domain = set of all real numbers
• Range = set of y values such that $y \ge 1$

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Explanation:

Use your favorite graphing tool to graph the equation. If your teacher doesn't allow you to use graphing software, then you'll have to plug in various x values to find the paired y values. This gives the set of (x,y) points needed to be plotted to form the parabola. The more points you plot, the more accurate the curve.

The graph is shown below. I used GeoGebra to make the graph. It's free graphing software. Desmos is another tool that I recommend.

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The lowest point on the parabola is the vertex (h,k) = (2,1) which is shown in the graph below.

This is due to the equation being in vertex form y = a(x-h)^2 + k. We see that h = 2 and k = 1.

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The axis of symmetry is the vertical line that passes through the vertex.

As such, the axis of symmetry equation is simply x = h. So that's how we get to x = 2.

In the graph below, the axis of symmetry is the red dashed line.

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There aren't any restrictions on x. We don't have to worry about dividing by zero or applying a square root to a negative number.

Therefore, any x value is allowed and the domain is the set of all real numbers.

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The range however isn't the set of all real numbers. The lowest y can get is y = 1 due to the vertex point. We can have y = 1 or larger

Therefore, $y \ge 1$ is the range.