Quadratic Functions Using Blocks

R2L3: Write the equation for the table

• y=(2)^x

• y=4x²

• y=2x²

• y=2x

Part I: Write an equation for the growth of the blocks. Part II: Show how this visual growth connects to equation. Part III: Find what figure # would result in 49 total blocks. Show work for this using your equation.

What type of function is represented in the table?

• linear

• exponential

• quadratic

• other

Select all the true statements about the diagram for the equation k(x) = 3x² + 2.

• There is 1 perfect square of x by x

• There are 2 perfect squares of x by x

• There are 3 perfect squares of x by x

• There are 2 extra rows of x-size

• There are 2 extra constant squares

Answer explanation

3x² means 3 perfect squares x by x.

• + 2 means there are 2 extra constant squares.

Which answer choice describes  y = -3x² +7x - 2 accurately?

• opens up with a maximum

• opens up with a minimum

• opens down with a maximum

• opens down with a minimum 

Then, plot the rest of the coordinates to show the entire graph shape, called a _____________________.

Answer explanation

The shape of a quadratic graph is always a PARABOLA. It is indeed a curve, but the specific vocabulary for the entire "arch" is parabola. This helps distinguish the shape from an exponential/geometric curve.

Using the equation f(x) = x² + 2x + 1, which of the following is the correct WORK when x = -3 to fill in the first row of the table?

• f(3) = (3)² + 2(3) + 1

  f(3) = 9 + 6 + 1

  f(3) = 16

• f(-3) = (-3)² + 2(-3) + 1

  f(-3) = 9 - 6 + 1

  f(-3) = 4

• f(-3) = (-3)² + 2(-3) + 1

  f(-3) = -9 - 6 + 1

  f(-3) = -14

Answer explanation

Careful with (-3)² = -3 * -3 = 9.

A negative times a negative is positive, so therefore any number squared will always be positive.

Identify the table as either linear, exponential, or quadratic.

• Linear

• Exponential

• Quadratic

Answer explanation

Quadratic because...

Linear first difference (-3,-1,+1,+3,+5,+7)

Constant second difference (+2)

Select the equivalent equation to h(x) = x(4x + 2)

• h(x) = 4x + 2

• h(x) = 4x² + 2

• h(x) = 4x² + 2x

• h(x) = 4x + 2x

Answer explanation

h(x) = x(4x + 2) can be multiplied using the distributive property.

x * 4x = 4x²

x * 2 = 2x

Therefore, h(x) = 4x² + 2x.

The first difference of this quadratic pattern is...

• Constant (+2)

• Linear (+5, +7, +9)

• There's no constant difference, it's multiplying each time.

Answer explanation

The FIRST difference of a quadratic pattern is always LINEAR.

The SECOND difference, or second layer of the pattern, shows the consistency of +2 (or whatever it is).