Unit 3C: Writing Quadratic Equations

When given 3 or more ordered pairs on a parabola, which of the following is a method you can use to find the equation in standard form?

• Make a table of values. Find the rate of change (slope) and y-intercept.

• On the calculator, use STAT-EDIT to enter the values into L₁ and L₂. Then go to STAT>CALC and choose "QuadReg" (option 5).

• 3 ordered pairs will not give you enough information to find the equation for the parabola.

Tags

CCSS.HSA.REI.D.11

Write the equation of the parabola shown.

• y = 2x² + 4x - 5
• y = 2x² - 4x + 5
• y = 2x² + 4x + 5
• y = 2x² - 4x - 5

Find the n^th term for the following quadratic sequence...

7, 13, 23, 37, 55...

• 2n² + 5

• 2n² + 5n

• n² + 5

• n² - 5

Tags

CCSS.HSA.CED.A.1

What is the equation for this parabola in factored form?

• y=(x+2)(x-1)
• y=(x-2)(x+1)
• y=(x-2)(x-1)
• y=(x+2)(x+1)

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

CCSS.HSA.SSE.B.3

Which function has the smaller minimum value, and why?

• The function g has the smaller minimum value because the minimum value of f is 6, and the minimum value of g is 2.

• The function g has the smaller minimum value because the minimum value of f is 6, and the minimum value of g is 5.

• The function f has the smaller minimum value because the minimum value of f is -10, and the minimum value of g is 2.

• The function f has the smaller minimum value because the minimum value of f is -10, and the minimum value of g is 5.

Approximately, what was the highest that the rocket flew?

• 6 feet

• 9 feet

• 3 feet

• It never flew.

Tags

CCSS.HSA.SSE.A.1

An object in launched directly upward at 64 feet per second (ft/s) from a platform 80 feet high. Its height is represented by the equation

s(t) = –16t² + 64t + 80

What will be the object's maximum height?

• 2 ft

• 80 ft

• 144 ft

• 64 ft

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.A.1

CCSS.HSF.IF.B.4

You jump off a 24 foot high cliff and your fall is modeled by the function:

h(t) = -16t² + 8t + 24

How long would it take you to hit the water?

• 8 seconds

• 1 second

• 1.5 seconds

• 1/4 second

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.4

A rock falls from the top of a cliff to the ocean 100 feet below. The distance, S, the rock is from the ocean as it falls is represented by the function S(t) = −16t² + 100, where t represents the number of seconds the rock has been falling. According to this function, how long does it take the rock to hit the water?

• 2.0 seconds

• 2.5 seconds

• 5.0 seconds

• 6.3 seconds

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

A ball is thrown from ground level straight up into the air at an initial velocity of 54 feet per second. The height of the ball tseconds after it is thrown is given by the formula h(t) = 54t − 16t². How many seconds after the ball is thrown will it return to the ground?

• 2.875

• 3.375

• 4

• 4.25