Graphing and Analyzing Quadratic Functions

Write the number of x-intercepts, number, and type of solution for the below graph (second graph: downward parabola not intersecting x-axis).

• Number of x-intercepts: 0 Number and type of solutions: 2 complex solutions

• Number of x-intercepts: 2 Number and type of solutions: 2 real solutions

• Number of x-intercepts: 1 Number and type of solutions: 1 real solution

• Number of x-intercepts: 0 Number and type of solutions: 1 real solution

Write the number of x-intercepts, number, and type of solution for the below graph (first graph: upward parabola intersecting x-axis at two points).

• Number of x-intercepts: 2 Number and type of solutions: 2 real solutions

• Number of x-intercepts: 1 Number and type of solutions: 1 real solution

• Number of x-intercepts: 0 Number and type of solutions: 2 complex solutions

• Number of x-intercepts: 2 Number and type of solutions: 2 complex solutions

Write the number of x-intercepts, number, and type of solution for the below graph (third graph: upward parabola tangent to x-axis at one point).

• Number of x-intercepts: 1 Number and type of solutions: 1 real solution (double root)

• Number of x-intercepts: 2 Number and type of solutions: 2 real solutions

• Number of x-intercepts: 0 Number and type of solutions: No real solutions

• Number of x-intercepts: 1 Number and type of solutions: 1 complex solution

Simplify and write −√36−√−81 as a complex number in a + bi form.

Hint: If negative is inside of a radical it turns into an i

• x = ±i√(169/121) = ±i(13/11)

• x = ±13/11

• x = ±i(11/13)

• x = ±13

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What is (9 - 3i) + (-17 - 9i)? (Show Work)

Hint: Stack like terms and combine

• -8 - 12i

• -26 - 6i

• 8 + 6i

• -8 + 12i

What is (4 - 3i)(-2 + 6i)?

Hint: Use the box method and remember 2 i's =-1

• 10 + 30i

• -10 + 30i

• 10 - 30i

• -10 - 30i

What is the complex conjugate of 12+186i? Write your answer in the form a + bi. Explain how you found the conjugate.

• Conjugate: 12 - 186i. Explanation: The complex conjugate is found by changing the sign of the imaginary part.

• Conjugate: 12 + 186i. Explanation: The complex conjugate is found by changing the sign of the real part.

• Conjugate: -12 - 186i. Explanation: The complex conjugate is found by changing both the real and imaginary parts.

• Conjugate: -12 + 186i. Explanation: The complex conjugate is found by changing only the real part.

• h(t) ≥ 45

• h(t) ≤ 45

• h(t) > 45

• h(t) < 45