Find the standard equation of a parabola that has a vertical axis and satisfies the given condit

step 1 We have given the vertex of a vertical axis parabola and its x intercept. And our question is to

Find the standard equation of a parabola that has a vertical...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Parabola

A parabola is a type of conic section that is defined as the set of all points equidistant from a fixed point called the focus and a fixed line called the directrix. It has a distinctive open, curved shape and can be oriented in different directions depending on its axis of symmetry.

Vertex Form of a Parabola

The vertex form of a parabola's equation is typically written as y = a(x - h)² + k, where (h, k) is the vertex of the parabola and 'a' determines the width and direction of the opening. This form is particularly useful because it directly shows the vertex and makes it easier to analyze the parabola's transformation from the basic y = x².

x-intercept

An x-intercept is a point where a graph crosses the x-axis, meaning that the y-coordinate at that point is zero. In the context of a parabola, knowing the x-intercepts can help determine key properties of its graph, such as symmetry and the distance from the vertex to the intercept.

Vertical Axis

When a parabola has a vertical axis, it means that its axis of symmetry is parallel to the y-axis. This orientation implies that the parabola opens upward or downward, and the standard vertex form y = a(x - h)² + k is especially applicable in these cases.

Transcript

Please give Ace some feedback