Quadratics Day 1

Quadratics Day 1

Algebra 1

X-Intercepts, zeros, roots and solutions

• These are all related.

• What we are looking for are the points where our graph crosses the x-axis.

• They can cross twice, just touch the x-axis , or they never touch the x-axis at all.

Multiple Choice

The following quadratic has how many zeros?

• 0

• 1

• 2

• 3

Multiple Choice

What are the zeros of x²+9x+14

• 2, 7
• -2, -7
• 2, -7
• -2, 7

Multiple Choice

Identify the solutions of the graph?

• x= 0 and x= -4

• x= 0 and x= 4

• y= 0

• x= 2

Domain 

• The domain of a function are the x-values.

• The domain of a quadratic function is all real numbers. Remember that a quadratic has arrows at the ends, which means it goes on forever in both directions

• Remember that a quadratic has arrows at the ends, which means it goes on forever in both directions.

Range

• The range of a function are the y-values.

• With a quadratic -there is either a minimum or a maximum y-value.

• That value helps us determine the range.

• Let's look at some examlples.......

Here is a graph with a maximum

Here is a quadratic with a minimum.

Multiple Choice

How many solutions does this graph have?

• one
• two
• no solutions
• cannot be determined

Multiple Choice

Identify the domain and range of the function.

• Domain: -6 ≤ x ≤ 2

  Range: -3 ≤ y ≤ 5

• Domain: All real number

  Range: -3 ≤ y ≤ 5

• Domain: All real numbers

  Range: y ≥ -3

• Domain: All real number

  Range: y ≤ -3

Multiple Choice

What is the domain and the range for the graph?

• Domain : -2 ≤ x ≤ 2
  Range : 0 ≤ y ≤ 4
• Domain : 0 ≤ x ≤ 4
  Range : -2 ≤ y ≤ 2
• Domain : All real #s
  Range : y ≤ 4
• Domain : -2 ≤ x ≤ 2
  Range : y ≤ 4

Multiple Choice

Find the y-intercept of f(x) = 2x² - 2x + 1

• 2
• -2
• 1
• -1

Multiple Choice

How many zeros does this parabola have? 

• 3
• 2
• 0
• 1

Finding a specific value on a function.

• When we are given a function:

   $f\left(x\right)=2x^2-5$ , sometimes we are asked to find specific value. Find  $f\left(2\right)$ .

• We enter this into Desmos!

Multiple Choice

Evaluate f(-2) when f(x)=x²+x-12

• -10
• 25
• -32

Multiple Choice

Evaluate f(-3) when f(x)=x²-2x+1

• 16
• -23
• -1

Multiple Choice

Evaluate f(3) when f(x)=x²+x-12

• 0
• 4
• -7