**Drawing parabolas**

- To find the y-intercept, put x = 0 into the equation and work out the y-coordinate.
- To find the x-coordinate, put y = 0 in the equation and solve the quadratic equation to get the x-coordinates.
- To find the vertex (turning point), add the x-intercepts together and divide by 2.

1

## What do you call the turning point of a parabola?

This property is

**called**symmetry. We say that the graph is symmetrical about the y-axis, and the y-axis is**called**the axis of symmetry. So, the axis of symmetry has equation x = 0. (0, 0) is**called**the**turning point**or vertex of the**parabola**.2

## What is the focus of a parabola?

A parabola is defined as follows: For a given

**point**, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus of points such that the distance to the focus equals the distance to the directrix.3

## What is the Y intercept of a parabola?

To find the x-intercept let y =

**0**and solve for x. You can solve for x by using the square root principle or the quadratic formula (if you simplify the problem into the correct form). Step 4: Graph the parabola using the points found in steps 1 – 3.4

## What is the turning point of a function?

A

**turning point**is a**point**at which the derivative changes sign. A**turning point**may be either a relative maximum or a relative minimum (also known as local minimum and maximum). If the**function**is differentiable, then a**turning point**is a stationary**point**; however not all stationary**points**are**turning points**.5

## What is the equation of a parabola?

The standard form is (x - h)

^{2}= 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p. If the parabola is rotated so that its vertex is (h,k) and its axis of**symmetry**is parallel to the x-axis, it has an equation of (y - k)^{2}= 4p (x - h), where the focus is (h + p, k) and the directrix is x = h - p.6

## What is the vertex form of a parabola?

f (x) = a(x - h)

^{2}+ k, where (h, k) is the**vertex**of the**parabola**. FYI: Different textbooks have different interpretations of the reference "standard**form**" of a quadratic function.7

## What is a parabola for?

A

**parabola**is a curve where any point is at an equal distance from: a fixed point (the focus ), and. a fixed straight line (the directrix )8

## How do you find the range of a parabola?

The values of a, b, and c

**determine**the shape and position of the**parabola**. The**domain**of a function is the set of all real values of x that will give real values for y. The**range**of a function is the set of all real values of y that you can get by plugging real numbers into x.9

## What is the formula for Vertex?

The

**vertex**form of a quadratic is given by. y = a(x – h)^{2}+ k, where (h, k) is the**vertex**. The "a" in the**vertex**form is the same "a" as. in y = ax^{2}+ bx + c (that is, both a's have exactly the same value). The sign on "a" tells you whether the quadratic opens up or opens down.10

## How do you find the minimum value of a function?

We can identify the

**minimum**or maximum**value**of a parabola by identifying the y-coordinate of the vertex. You can use a graph to identify the vertex or you can**find**the**minimum**or maximum**value**algebraically by using the formula x = -b / 2a. This formula will give you the x-coordinate of the vertex.11

## What is the axis of symmetry of a parabola?

The graph of a quadratic function is a

**parabola**. The**axis of symmetry**of a**parabola**is a vertical line that divides the**parabola**into two congruent halves. The**axis of symmetry**always passes through the vertex of the**parabola**. The -coordinate of the vertex is the equation of the**axis of symmetry**of the**parabola**.12

## How do you find the axis of symmetry of a parabola?

**Characteristics of the axis of symmetry include the following:**

- It is the line of symmetry of a parabola and divides a parabola into two equal halves that are reflections of each other about the line of symmetry.
- It intersects a parabola at its vertex.
- It is a vertical line with the equation of x = -b/2a.

13

## How do you find the vertex of a quadratic function?

**Method 1**

**Using the Vertex Formula**

- Identify the values of a, b, and c.
- Use the vertex formula for finding the x-value of the vertex.
- Plug the x-value into the original equation to get the y-value.
- Write down the x and y values as an ordered pair.

14

## What is the vertex of the graph?

The

**vertex**of a parabola is the point where the parabola crosses its axis of symmetry. If the coefficient of the term is positive, the**vertex**will be the lowest point on the**graph**, the point at the bottom of the “ ”-shape.15

## What is the definition of a vertex?

From Latin:

**vertex**"highest point" Definition: The common endpoint of two or more rays or line segments.**Vertex**typically means a corner or a point where lines meet. For example a square has four corners, each is called a**vertex**. The plural form of**vertex**is**vertices**.16

## What are the axis of symmetry?

A line of

**symmetry**for a graph. The two sides of a graph on either side of the**axis of symmetry**look like mirror images of each other. Example: This is a graph of the parabola y = x^{2}– 4x + 2 together with its**axis of symmetry**x = 2. The**axis of symmetry**is the red vertical line.17

## What is a quadratic graph?

So, given a

**quadratic**function, y = ax^{2}+ bx + c, when "a" is positive, the parabola opens upward and the vertex is the minimum value. On the other hand, if "a" is negative, the**graph**opens downward and the vertex is the maximum value.18

## Which function is a quadratic function?

Graphs. A

**quadratic function**is one of the form f(x) = ax^{2}+ bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a**quadratic function**is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape.19

## What is the name of the shape of the graph of a quadratic function?

The

**graph of a quadratic function**is**called**a parabola and has a curved shape. One of the main points of a parabola is its vertex. It is the highest or the lowest point on its**graph**. You can think of like an endpoint of a parabola.20

## What is the turning point of the story?

The five elements of plot are the exposition, rising action, climax, falling action and resolution or denouement. The climax is the

**turning point**of the**story**, the**point**to which the rising action has been building and the**point**at which the characters have what they need to resolve the conflict.