🔊 Review and Quadratics 2

🔊 Quadratics 2

look at the applications

The parts of a parabola: how do you describe them

• y-intercept

• x-intercepts

• vertex

Las partes de una parábola: cómo las describes

• intersección con el eje y

• intersección con el eje x

• vértice

But FIRST

SOME REVIEW

Multiple Choice

Which of the following is an example of a quadratic function?

Multiple Choice

What is the vertex of the graph?

• (2,4)
• (-2,-4)
• (4,2)
• (-4,-2)

Multiple Choice

What are the X-intercept(s) of this graph?

• (-3, 4)

• -3

• 1 and 3

• (2, 1)

Multiple Choice

What is another word for zeros?

• y-intercepts
• roots
• vertex
• axis of symmetry

Multiple Choice

Maximum or Minimum

• Maximum

• Minimum

Multiple Choice

y-intercept

• 1

• -1/2

Multiple Choice

x-intercepts

• -4 and 0

• -1 and -2

Multiple Choice

Name the Vertex

• (3, -4)

• (-3, -4)

Multiple Choice

Name the vertex

• (1,1)

• (0,0)

The equation that connects to this pattern is

•  $y=x^2$  

• the figure number is the same as the dimensions of the square

La ecuación que se conecta a este patrón es

•  $y=\left(x+1\right)^2$  

• the figure number + 1 is the same as the dimensions of the square

• el número de figura + 1 es el mismo que las dimensiones del cuadrado

The equation that connects to this pattern is

•  $y=\left(x+1\right)^2+1$  

• How is it connected to the pattern on the slide before?

• What is the same? What is different?

The equation that connects to this pattern is

•  $y=\left(x+1\right)^2+2$  

• What is the same? 

• What is different?

Open Ended

How is the pattern connected to the pattern on the slide before?

Open Ended

What does figure 4 look like?

Open Ended

What does figure 13 look like?

Open Ended

What does figure 0 look like?

Multiple Choice

What factors were multiplied in order to get the product shown by the algebra tiles above?

• (x+2)(x+3)

• (x-6)(x+1)

• (x-2)(x-3)

• (x-2)(x+3)

Multiple Choice

What equation connects to this pattern?

• $y=x^2$

• $y=x^2+x$

• $y=x^2+3$

• $y=x^2+4$

Multiple Choice

What equation connects to this pattern?

• $y=x^2$

•  $y=x^2-x$ 

•  $y=x^2-1$ 

•  $y=x^2-2$ 

Multiple Select

What are the missing pieces of the "box" shown?

•  $-7x$  

• 7x

• 28

• -28

Multiple Choice

What is the leading coefficient?

• Positive
• Negative
• Even
• Odd

Multiple Choice

What is the leading coefficient?

• Positive
• Negative
• Odd
• Even

Multiple Choice

What is the leading coefficient?

• Positive
• Negative
• Odd
• Even

Multiple Choice

What is the leading coefficient?

• Positive 
• Negative
• Odd 
• Even

Multiple Choice

What is the degree?

• Positive 
• Negative
• Odd 
• Even

Multiple Choice

What is the degree?

• Positive 
• Negative
• Odd 
• Even

Multiple Choice

What is the degree?

• Positive
• Negative
• Odd
• Even

Multiple Choice

What is the degree?

• Positive
• Negative
• Odd
• Even

Now for the applications

What does the graph and equation tell us?

Find at least three things.

Open Ended

What does the equation and the graph tell us?

What does the graph and equation tell us?

The ball starts on the ground (0,0)

It hits the ground at 6.25 seconds (6.25, 0)

The maximum height of the ball is just over 150 feet after about 3 seconds (3.3, 152)

The launch speed of the golf ball is 100 feet per second,

Poll

In how many of the details do you see the connection between the graph/equation and the situation?

• 4

• 3

• 2

• 1

What does the graph tell us?

Open Ended

What does the graph tell us?

What you tell me about this?

The path of a rocket is given by the equation: $h=-16t^2+128t$  

Open Ended

Write down and many things as you can about the graph, the equation and the situation.

 $h=-16t^2+128t$  

Multiple Select

Which of the following are true statements about the rocket?

• It starts on the ground.

• It reaches a height of 256 feet

• It takes 3 seconds to reach maximum height.

• It takes 8 seconds to hit the ground.

• The launch speed is 128 feet per second.

What do the equation and the graph say?

A rocket will fall into the lake after exploding at its maximum height. The rocket’s height above the surface of the lake is given by the function

 $y=-16x^2+64x+80$  

Open Ended

How is the graph connected to the equation?

 $y=-16x^2+64x+80$  

Multiple Select

Which of theses statements about the rocket are true?

• You know the launch pad is 80 feet above the lake because of the +80 in the equation.

• You know the launch pad is 80 feet above the lake because of the y-intercept is 80.

• The rocket explodes after 2 seconds.

• The Height at explosion is about 145 feet.

• The rocket has a launch speed of 64 feet per second

A rock is thrown from the top of a tall building. The distance, in feet, between the rock and the ground t seconds after it is thrown is given by

 $d(t)=-16t^2–4t+382.$  

Open Ended

How are the graph, equation and situation connected? $d(t)=-16t^2–4t+382.$ 

Multiple Select

Which statements about the rock are true?

• It takes about 5 seconds for the rock to hit the ground.

• The x- intercept is (4.8, 0) this tells me the rock hits the ground at 4.8 seconds

• The building is 382 feet tall.

• The y-intercept is (382,0)

• The rock lands 4.8 feet away (at the x-intercept)

Another rocket

A model rocket is launched from the front yard. Its flight path is modeled by

 $y=-16x^2+45x+2$  

Open Ended

How are the graph, equation and situation connected? $y=-16x^2+45x+2.$ 

Multiple Select

Which statements are true?

 $y=-16x^2+45x+2.$  

• There is a 2 foot launch pad.

• The launch speed is 45 feet per second.

• The launch speed is 16 feet per second

• The -16 is the effect of gravity in the model

• The negative leading term (-16) indicates the graph opens down.

Here is a new type of situation.

The profit from selling honey is  modelled by the following equation,  $P\left(t\right)=-17t^2+2040t+121$  

Maximum Profit happens at the vertex of the parabola

The profit from selling honey is  modelled by the following equation,  $P\left(t\right)=-17t^2+2040t+121$  

Open Ended

What can you tell from the profit graph?

Multiple Select

What questions could you answer using the graph or equation?

 $P\left(t\right)=-17t^2+2040t+121$ 

• What is the maximum profit?

• What is the minimum profit

• How many day into the production cycle will the maximum profit happen?

• How many day into the production cycle will the minimum profit happen?

Poll

This material was helpful.

• Yes and I understood it.

• Yes and I would like more practice.

• No, I knew all of this material and got 100% on all of the questions.