Questions: Graph the function. h(x)=2 x^2-1 Plot five points on the graph of the function: one point with x=0, two points with x>0, and two points with x<0.

Transcript text: Graph the function. \[ h(x)=2 x^{2}-1 \] Plot five points on the graph of the function: one point with $x=0$, two points with $x>0$, and two points with $x<0$.

Solution

Solution Steps

Step 1: Find the vertex

When $x=0$, $h(0)=2(0)^2-1=-1$. So the vertex is at $(0, -1)$.

Step 2: Choose x-values and find corresponding y-values

We need five points. We already have the vertex $(0,-1)$. Let's pick two x-values to the left and two to the right of the vertex.

If $x=-2$, $h(-2)=2(-2)^2-1=2(4)-1=7$. So, $(-2,7)$ is a point on the graph. If $x=-1$, $h(-1)=2(-1)^2-1=2(1)-1=1$. So, $(-1,1)$ is a point on the graph. If $x=1$, $h(1)=2(1)^2-1=2(1)-1=1$. So, $(1,1)$ is a point on the graph. If $x=2$, $h(2)=2(2)^2-1=2(4)-1=7$. So, $(2,7)$ is a point on the graph.

Step 3: Plot the points and graph the parabola

The five points are $(0,-1)$, $(-2,7)$, $(-1,1)$, $(1,1)$, and $(2,7)$. Plot these points on the graph and connect them with a smooth curve to form a parabola.

Final Answer:

The graph of the function $h(x) = 2x^2 - 1$ is a parabola that opens upwards with its vertex at $(0,-1)$ and passes through the points $(-2,7)$, $(-1,1)$, $(1,1)$, and $(2,7)$.

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