# What is graphing quadratic functions?

## What is graphing quadratic functions?

The graph of a quadratic function is a U-shaped curve called a parabola. The sign on the coefficient a of the quadratic function affects whether the graph opens up or down. The x-intercepts are the points at which the parabola crosses the x-axis.

### What is a vertical shift in a quadratic function?

You can represent a vertical (up, down) shift of the graph of f(x)=x2 f ( x ) = x 2 by adding or subtracting a constant, k . f(x)=x2+k. If k>0 , the graph shifts upward, whereas if k<0 , the graph shifts downward.

What are the 3 forms of quadratic functions?

Read below for an explanation of the three main forms of quadratics (standard form, factored form, and vertex form), examples of each form, as well as strategies for converting between the various quadratic forms.

What are examples of quadratic functions?

Examples of quadratic equations in other forms include:

• x(x – 2) = 4 [upon multiplying and moving the 4, becomes x² – 2x – 4 = 0]
• x(2x + 3) = 12 [upon multiplying and moving the 12, becomes 2x² – 3x – 12 = 0]
• 3x(x + 8) = -2 [upon multiplying and moving the -2, becomes 3x² + 24x + 2 = 0]

## What is the quadratic parent function?

The parent function of the quadratic family is f(x) = x2. A transformation of the graph of the parent function is represented by the function g(x) = a(x − h)2 + k, where a ≠ 0.

### What are the 3 forms of a quadratic equation?

The 3 Forms of Quadratic Equations

• Standard Form: y = a x 2 + b x + c y=ax^2+bx+c y=ax2+bx+c.
• Factored Form: y = a ( x − r 1 ) ( x − r 2 ) y=a(x-r_1)(x-r_2) y=a(x−r1)(x−r2)
• Vertex Form: y = a ( x − h ) 2 + k y=a(x-h)^2+k y=a(x−h)2+k.

How do you do a vertical shift down?

We can express the application of vertical shifts this way: Formally: For any function f(x), the function g(x) = f(x) + c has a graph that is the same as f(x), shifted c units vertically. If c is positive, the graph is shifted up. If c is negative, the graph is shifted down.

How do you find the shift of a quadratic function?

The graph of y=(x-k)²+h is the resulting of shifting (or translating) the graph of y=x², k units to the right and h units up. For example, y=(x-3)²-4 is the result of shifting y=x² 3 units to the right and -4 units up, which is the same as 4 units down.

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