4 Mid-Chapter Quiz

Do you know HOW?

Graph each function.

1. y = 4 x 2 + 16 x + 7 y equals , 4 x squared , plus 16 x plus 7
2. y = ( x + 8 ) 2 − 3 y equals open x plus 8 , close squared , minus 3
3. y = − ( x + 2 ) 2 − 7 y equals negative open x plus 2 , close squared , minus 7
4. y = − 3 x 2 − 2 x + 1 y equals negative 3 , x squared , minus 2 x plus 1

Identify the axis of symmetry, maximum or minimum value, and the domain and range of each function.

5. y = − x 2 + 6 x + 5 y equals negative , x squared , plus 6 x plus 5
6. y = 1 2 ( x − 6 ) 2 + 7 y equals , 1 half . open x minus 6 close squared . plus 7
7. y = − 3 ( x + 2 ) 2 + 1 y equals negative 3 . open x plus 2 close squared . plus 1
8. y = 4 x 2 − 8 x y equals , 4 x squared , minus 8 x
9. Rewrite the equation y = − 3 x 2 − 6 x − 8 y equals negative 3 , x squared , minus 6 x minus 8  in vertex form. Identify the vertex and the axis of symmetry of the graph.

Write each expression in factored form.

10. 16 − 2 m 2 16 minus , 2 m squared
11. − x 2 + 3 x negative , x squared , plus 3 x
12. y 2 − 13 y + 12 y squared , minus 13 y plus 12
13. k 2 − 5 k − 24 k squared , minus 5 k minus 24
14. 4 y 2 − 9 4 y squared , minus 9
15. − 10 n + 25 + n 2 negative 10 n plus 25 plus , n squared
16. 2 x 2 + 7 x + 6 2 x squared , plus 7 x plus 6

Find a quadratic model in standard form for each set of values.

17. (0, 3), (1, 10), (2, 19)
18. (0, 0), ( 1 , − 5 ) , open 1 comma negative 5 close comma  (2, 0)

Write the equation of each parabola in vertex form.

Do you UNDERSTAND?

21. Write the expression 3 x 4 − 12 x 3 − 36 x 2 3 x to the fourth , minus , 12 x cubed , minus , 36 x squared  in factored form. Explain how you know the expression is completely factored.
22. Open-Ended Write the equation of a parabola with a vertex at (3, 2). Name the axis of symmetry and the coordinates of two other points on the graph.
23. Writing Explain how to factor 25 x 2 − 30 x + 9 . 25 x squared , minus 30 x plus 9 .
24. Reasoning Write the equation of two parabolas such that they have a common vertex and are reflections of each other across the x-axis.
25. Write the equation of a parabola in standard form and explain how to convert it to vertex form. How would you reverse the process?
26. What is the relationship between the x-intercepts of the graph of a quadratic function and the x-coordinate of the vertex of that graph? Explain how you determined your answer.

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