Find the y-Intercept and the x-intercept of the line below. Click on "None" if applicable.

Mathematics

1 answer:

Eva8 [605]2 years ago

3 0

Answer:

Y-intercept: -1 (0,-1)

X-intercept: -4 (-4,0)

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Write the equation of the circle with the given graph.

lara [203]

By identifying the radius and the center, we concluded that the equation is something like:

$(x - 2)^2 + (y - 1.5)^2 = 1.8^2$

<h3></h3><h3>How to write the equation of the circle?</h3>

For a circle centered on the point (a, b) with a radius R, the equation is:

$(x - a)^2 + (y - b)^2 = R^2$

So first we need to identify the center, we can see that it is: (2, 1.5)

And the radius is the distance between the center and the edge.

R = 1.8 (measured with a ruler, respecting the notation of the graph).

Then the equation of the circle is something like:

$(x - 2)^2 + (y - 1.5)^2 = 1.8^2$

If you want to learn more about circles:

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write a linear equation that intersects y=x^2 at two points. Then write a second linear equation that intersects y=x^2 at just o

Liula [17]

We know that $y = x^2$ is a parabola, concave up, with vertex in the origin $(0,0)$

So, we may use three horizontal lines for our purpose: any horizontal line above the x axis will intersect the parabola twice. The x axis itself intersects the parabola once on the vertex, while any horizontal line below the x axis won't intercept the parabola.

Here's the examples:

The horizontal line $y = 4$ intercepts the parabola twice: the system $y = x^2,\ y = 4$ is solved by $x^2=4 \implies x = \pm 2$
The horizontal line $y=0$ intercepts the parabola only once: the system is $y=x^2,\ y=0$ which yields $x^2=0\implies x=0$ which is a repeated solution
The horizontal line $y=-5$ intercepts the parabola only once: the system is $y=x^2,\ y=-5$ which yields $x^2=-5$ which is impossible, because a squared number can't be negative.