What happens when the vertex is on the x-axis?

If the vertex of a parabola is on the x-axis, then because the parabola should intersect the x-axis at with the y-coordinate being . Therefore, in this type of parabola, vertex form should be: The parabola is factorable into a binomial with multiplicity 2 and can be multiplied by a constant.

What does it mean when a parabola is reflected in the x-axis?

On the screen you can see that the graph of this equation is a parabola. The reflection of such a parabola over the x-axis is simply written as y = -(x^2). In other words, the function of f(x) becomes -f(x) when reflected over the x-axis. When reflected everything looks like an upside down version of our parent graph.

When parabola is about the x-axis?

Standard Forms of Parabolas with Vertex (0, 0) (Figure) and (Figure) summarize the standard features of parabolas with a vertex at the origin. Figure 5. (a) Whenp>0 and the axis of symmetry is the x-axis, the parabola opens right. (b) Whenp<0 and the axis of symmetry is the x-axis, the parabola opens left.

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.

When the vertex is on the y-axis?

As we can see from this set of parabolas, the vertex is displaced from the y-axis as b is changed. When b = 0 (orange), the vertex is on the y-axis. When b > 0, the vertex is to the left of the y-axis and when b < 0, the vertex is to the right of the y-axis.

What is the rule for reflection over x-axis?

The rule for a reflection over the x -axis is (x,y)→(x,−y) .

Where is the vertex parabola?

The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry. For a parabola whose equation is given in standard form , the vertex will be the minimum (lowest point) of the graph if and the maximum (highest point) of the graph if .

What does a vertex represent?

vertex: The point at which a parabola changes direction, corresponding to the minimum or maximum value of the quadratic function.

What is a vertex of a parabola?

The vertex of a parabola is the point where the parabola crosses its axis of symmetry. If the coefficient of the x2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “ U ”-shape. In this equation, the vertex of the parabola is the point (h,k) .