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Five Question Mixed Review

Five Question Mixed Review. 1. What is this function: y= 3x-2 2. What is the y-intercept of the above equation? Solve for x: 16 = 5x + 1 What is the slope of this equation: y= ½ x + 9 Write this equation in function notation: y = 6p - 7.

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Five Question Mixed Review

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  1. Five Question Mixed Review 1. What is this function: y= 3x-2 2. What is the y-intercept of the above equation? • Solve for x: 16 = 5x + 1 • What is the slope of this equation: y= ½ x + 9 • Write this equation in function notation: y = 6p - 7

  2. Five Question Mixed Review--Key • Linear • -2 • 16 = 5x + 1 15 = 5x 3 = x or -1 -1 5 5 x = 3 15 = 5x • ½ • f(p) = 6p - 7

  3. Parabolas: Nature or by Design Ideas? What on Earth is a parabola?

  4. Can you find the parabolic shapes?

  5. Standard and Essential Questions MM1A1b: Graph the basic functions f(x) = xn Essential Question: Can you identify a quadratic function by its components? parts

  6. A quick look at the shape: So what do we notice? Does it point up or down? What shape? How is it different from a linear graph? Could you predict what it will look like with just 2 points? Is the slope constant? If not, what is it?

  7. What is a parabola? KEY NOTE CARD: A parabola is the U-shaped graph. It can be pointing up (positive slope) or pointing down (negative slope).

  8. A quick look at an equation The most basic quadratic formula is y = x2 it is called a parent graph. This means that the U shape (a parabola) is turned up and the vertex is at (0,0).

  9. The equation for this graph Is y = x2 This is a quadratic parent graph. Notice where the vertex is located (0,0) Remember: A vertex is where the quadratic graph turns and shifts direction. It is also called a critical point.

  10. What does an input/output chart look like for this parent graph? Ponderables What do you notice? Do x values repeat? Do y values repeat? What do you call an image like this? Can you see the vertex? What do you notice about the slope?

  11. What Changed? The vertex moved! When a number is changed here, it shows how the graph moves up and down. It moved up by one unit!

  12. This quadratic graph moved DOWN one unit. New vertex: (0, -1)

  13. Name that shift!

  14. Name this shift!

  15. Shifting up and down along the y-axis is called vertical shift. BUT you can also shift left and right along the x-axis? What is it called?

  16. This is called a horizontal (left/right) shift. The parent graph shifted to the left 1 unit. The new equation would look like this: y = (x+1)2 Horizontal movement is always inside the parentheses with the x. These equations have a trick though—you move in the opposite direction! New vertex: (-1,0)

  17. Name that shift! What kind is it? What is the new vertex?

  18. Name this shift! What kind is it? What is the new vertex?

  19. This graph shifts both ways! What is the vertical shift? What is the horizontal shift? What is the vertex?

  20. How about this one? What is the vertical shift? What is the horizontal shift? What is the vertex? Notice how the equation matches the vertex except for the opposite sign inside the parentheses?

  21. Identifying the Slope Slope = rise/run = IT’S A FACT: In a parent graph the vertex is at (0,0) and the slope of the FIRST reflective points are 1. The rest of the slope is VARIABLE or CHANGING H Slope = 5 Slope = 3 Slope = 1

  22. What happens if the slope is more than 1? Slope = 4 How does it compare to the parent graph?

  23. Slope = -4 What happened?

  24. Slope = ½ How does this compare to the parent graph?

  25. Slope = -½ How does this compare to the last graph?

  26. Parts of a Quadratic Equation Horizontal shift = _2__ (Opposite of x vertex value) y- intercept vertical shift = _2__ Slope= __2_ When the slope is larger than 1 then the graph becomes… Vertex can be found at (2, 2)

  27. Graphic Organizer: Parts of a Quadratic Equation _______ shift (Opposite of__ vertex value) ______ _________ _______shift Vertex can be found at (__, __)

  28. Parts of a Quadratic Equation Horizontal shift=___ (Opposite of x vertex value) y- intercept vertical shift= ___ Slope = ___ Vertex can be found at (__, __)

  29. Parts of a Quadratic Equation Horizontal shift=___ (Opposite of x vertex value) y- intercept vertical shift= ___ Slope = ___ When the slope is smaller than 1 then the graph becomes… Vertex can be found at (__, __)

  30. Parts of a Quadratic Equation Horizontal shift=___ (Opposite of x vertex value) y- intercept vertical shift= ___ Slope = ___ Vertex can be found at (__, __) Does it matter how large the numbers are?

  31. Get with a partner to do these! • Directions: • Identify the • Slope • y-intercept • Vertex • AND • Graph 1 of these!

  32. Partner task--Key • Directions: • Identify the • Slope • y-intercept • Vertex • AND • Graph 1 of these! Ex. y=x2-2

  33. Quiz Graphing Quadratic Functions 1-8. Choose the function rule that matches the graph. Put the letter in the blank. • Which of the graphs above is the parent graph for quadratic functions? #______ • How many graphs have a negative slope?____ 1. 5. 2. 6. 3. 7. 4. 8.

  34. Quiz Graphing Quadratic Functions--Key 1-8. Choose the function rule that matches the graph. Put the letter in the blank. • Which of the graphs above is the parent graph for quadratic functions?#___4___ • How many graphs have a negative slope?__2__ 1. 5. 2. 6. 3. 7. 4. 8.

  35. Extending/Refining

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