Questions: Select the graph that shows the relation: x=y^2-5.

Solution Steps

To solve the problem of selecting the graph that shows the relation $x = y^2 - 5$, we need to understand the shape and orientation of the graph. This equation represents a parabola that opens to the right because $x$ is expressed in terms of $y$. The vertex of the parabola is at $( -5, 0 )$.

The given equation is: $$x = y^2 - 5$$

This is a quadratic equation in terms of $y$. To understand the graph of this equation, we need to analyze its properties.

The equation $x = y^2 - 5$ represents a parabola. Since $y$ is squared, the parabola opens horizontally. Specifically, it opens to the right because the coefficient of $y^2$ is positive.

The vertex of the parabola can be found by setting $y = 0$: $$x = 0^2 - 5 = -5$$ So, the vertex is at the point $(-5, 0)$.

To better understand the graph, we can plot a few key points by substituting values for $y$:

• When $y = 1$: $$x = 1^2 - 5 = -4$$ Point: $(-4, 1)$

• When $y = -1$: $$x = (-1)^2 - 5 = -4$$ Point: $(-4, -1)$

• When $y = 2$: $$x = 2^2 - 5 = -1$$ Point: $(-1, 2)$

• When $y = -2$: $$x = (-2)^2 - 5 = -1$$ Point: $(-1, -2)$

Using the vertex and the key points, we can sketch the graph. The parabola opens to the right with the vertex at $(-5, 0)$ and passes through the points $(-4, 1)$, $(-4, -1)$, $(-1, 2)$, and $(-1, -2)$.

Final Answer