What is the point of intersection of the x-axis and the y-axis?

The point where the x- and y-axis intersect is called the origin.

Is it possible for a parabola to not intersect the x-axis?

If the discriminant of a quadratic function is less than zero, that function has no real roots, and the parabola it represents does not intersect the x-axis.

When the Vertex is the only point that touches the x-axis?

If the vertex lies on the x-axis (yvertex=0), then the parabola has exactly one x-intercept and it’s the vertex. For all other cases, the parabola will have two x-intercepts. You find them by factoring the quadratic equation or by using the quadratic formula.

Can a parabola cross the Y-axis twice?

A parabola can cross the x-axis once, twice, or never. These points of intersection are called x-intercepts.

Which of the following is defined to be the point of intersection of the X & y-axis Brainly?

The intersection of the two axes is known as the originThe point where the x- and y-axes cross, denoted by (0, 0)., which corresponds to the point (0, 0).

Why do some parabolas have no x intercepts?

Since a 0 the parabola opens up (is U shaped). Since the roots are imaginary the parabola has no x-intercepts.

How do you prove a graph does not intersect the x-axis?

To find where the graph intersects the x axis we solve the equation f(x) = 0 or y = 0 as all points on the x axis have y = 0. Again we get an equation that has no solution so we conclude that the graph does not intersect the x axis.

Does the graph of every function crosses the y-axis exactly once?

The y-intercept of the line is b. This is the y value where the line crosses the y-axis (when the x = 0). Notice that a line crosses each axis only once (at most). This graph represents a quadratic function, which is y = ax2 + bx + c.

What do you call the intersection of the x-axis and y-axis in the rectangular coordinate system?

The origin
The origin is the intersection of the x and y-axes. The Cartesian coordinates of a point in the plane are written as (x,y). The first number x is called the x-coordinate (or x-component), as it is the signed distance from the origin in the direction along the x-axis.

How to find the number of points where the parabola intersects the x-axis?

We may find number of points where the parabola intersects the x-axis, using the formula for discriminant. Let us look into some examples to understand the above concept. Without sketching the graphs, find whether the graphs of the following functions will intersect the x-axis and if so in how many points.

How do you graph parabolas with vertex other than the origin?

To graph parabolas with a vertex other than the origin, we use the standard form for parabolas that have an axis of symmetry parallel to the x -axis, and for parabolas that have an axis of symmetry parallel to the y -axis. These standard forms are given below, along with their general graphs and key features.

What are the key features of a parabola?

(c) When and the axis of symmetry is the y -axis, the parabola opens up. (d) When and the axis of symmetry is the y -axis, the parabola opens down. The key features of a parabola are its vertex, axis of symmetry, focus, directrix, and latus rectum.

What is the dashed line with each parabola called?

The dashed line with each of these parabolas is called the axis of symmetry. Every parabola has an axis of symmetry and, as the graph shows, the graph to either side of the axis of symmetry is a mirror image of the other side.