Equivalent Forms of Quadratic Functions

What is the equation of this graph?

• f(x) = (x -5)² + 1

• f(x) = (x - 1)² - 5

• f(x) = (x + 1)² - 5

• f(x) = (x + 5)² +1

If the blue is f(x)=x^2, then the red must be

• g(x)=x²-5

• g(x)=x²+5

• g(x)=(x-5)²

• g(x)=(x+5)²

What is the arrow pointing at? How can you use this value?

• The arrow is pointing at the y-intercept. The x-value is the axis of symmetry and the y-value of this point is equivalent to the maximum/minimum 

• The arrow is pointing at the vertex. The x value of this point is equivalent to the maximum/minimum and the y-value is the axis of symmetry

• The arrow is pointing at the solution. The y value of this point is equivalent to the maximum and the x value is equivalent to the minimum

• The arrow is pointing at the vertex. The x-value is the axis of symmetry and the y-value is equivalent to the minimum/maximum

Convert the equation y= x²-2x-5 into vertex form. 

• y= (x-1)²-6

• y= -(x-1)²-6

• y= (x+1)²-6

• y= -(x+6)²-1

Which equation is equivalent to ( y = x^2 + 24x - 18 )?

• ( y = (x + 12)^2 - 162 )

• ( y = (x + 12)^2 + 126 )

• ( y = (x - 12)^2 - 162 )

• ( y = (x - 12)^2 + 126 )

Which of the following represents a quadratic function?

Write the equation into standard form

Mathematical Equivalence

ON

The graph of a quadratic function is shown. Write a quadratic equation in standard form to represent the graph.

Mathematical Equivalence

ON

A table of values for a quadratic function is shown.

Type the equation of the quadratic function in Standard Form.

y = ax² + bx + c

Mathematical Equivalence

ON

Mathematical Equivalence

ON