## What is a parabola that opens downward?

If a<0 in f(x)=ax2+bx+c, the **parabola opens downward**. In this case the vertex is the maximum, or highest point, of the **parabola**. Again, a large negative value of a makes the **parabola** narrow; a value close to zero makes it wide.

## What is it called when a parabola opens up?

are **called parabolas**. The vertex of a **parabola opening upward** is also **called** the minimum point. The vertex of a **parabola opening** downward is also **called** the maximum point. The x-intercepts are **called** the roots, or the zeros.

## What do you call the highest point of a parabola that opens downward?

If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value. In either case, the vertex is a turning point on the graph. The graph is also symmetric with a vertical line drawn through the vertex, called **the axis** of symmetry.

## What is the standard form of a parabola that opens up or down?

The directrix is the line y = k – p. The axis is the line x = h. If p > 0, the **parabola opens upward**, and if p < 0, the **parabola opens downward**. If a **parabola** has a horizontal axis, the **standard form** of the **equation** of the **parabola** is this: (y – k)^{2} = 4p(x – h), where p≠ 0.

## How do you tell if a parabola opens upward or downward?

There is an easy way to **tell whether** the graph of a quadratic function **opens upward or downward**: **if** the leading coefficient is greater than zero, the **parabola opens upward**, and **if** the leading coefficient is less than zero, the **parabola opens downward**.

## How do you tell if a parabola opens left or right?

**Let’s look at a few key points about these patterns:**

**If**the x is squared, the**parabola**is vertical (**opens**up or down).**If**the y is squared, it is horizontal (**opens left or right**).**If**a is positive, the**parabola opens**up or to the**right**.**If**it is negative, it**opens**down or to the**left**.- The vertex is at (h, k).

## What is a parabolic curve?

In mathematics, a **parabola** is a plane **curve** which is mirror-symmetrical and is approximately U-shaped. The **parabola** is the locus of points in that plane that are equidistant from both the directrix and the focus.

## What does the A represent in a parabola?

For graphing, the leading coefficient “a” indicates how “fat” or how “skinny” the **parabola** will be. **Parabolas** always have a lowest point (or a highest point, if the **parabola** is upside-down). This point, where the **parabola** changes direction, is called the “vertex”.

## How do you know if an equation is a parabola?

**If** they are, then these characteristics are as follows:

- Circle.
**When**x and y are both squared and the coefficients on them are the same — including the sign. **Parabola**.**When**either x or y is squared — not both.- Ellipse.
**When**x and y are both squared and the coefficients are positive but different. - Hyperbola.

## How do you know if a parabola is maximum or minimum?

**If** the **parabola** opens up, the vertex represents the lowest point on the graph, or the **minimum** value of the quadratic function. **If** the **parabola** opens down, the vertex represents the highest point on the graph, or the **maximum** value.

## What is the top point of a parabola?

A **parabola** which opens up has a lowest **point** and a **parabola** which opens down has a **highest point**. The **highest** or lowest **point** on a **parabola** is called the vertex.

## Why is a parabola a strong shape?

Why is the **parabola** considered such a **strong shape**? The **parabola** is considered such a **strong shape** because of its natural oval **shape**. Both ends are mounted in a fixed bearing while the arch has a uniformly distributed load. When an arch carries only its own weight, the best **shape** is a catenary.

## What is the C in standard form?

The standard form for linear equations in two variables is Ax+By=C. For **example**, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it’s pretty easy to find both intercepts (x and y). This form is also very useful when solving systems of two linear equations.

## How do you turn a parabola into standard form?

Not all equations come packaged that way, though. You may have to do some work on the equation first to be able to identify anything about the **parabola**. The **standard form** of a **parabola** is (x – h)^{2} = a(y – k) or (y – k)^{2} = a(x – h), where (h, k) is the vertex.

## What is standard form of a quadratic function?

The quadratic function f(x) = a(x – h)^{2} + k, a not equal to zero, is said to be in standard form. If a is positive, the graph opens upward, and if a is negative, then it opens downward. The line of symmetry is the vertical line x = h, and the vertex is the **point** (h,k).