Textbook

Functions 11 McGraw Workbook
Chapter

Chapter 1
Section

Chapter 1 Related Competition Problems

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Solutions
10 Videos

The graph of `y = -x^2-5x + 36`

intersects the x-axis at two points, A and B. The length of line segment AB is

A. 9

B. 13

C. 5

D. 36

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Q1

If `f(x)=x^2+5x+3k`

and `f(k)=-16`

, `f(2)`

equals

A. -4

B. -16

C. -2

D. 2

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Q2

The minimum distance between the parabolas `y = -5x^2 - 8`

and `y = 7x^2 + 6`

is

A. 14

B. 12

C. 8

D. 6

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Q3

A quadratic function of the form `f(x) = ax^2 + bx + c`

has roots
`x = \frac{-3 \pm \sqrt{31}}{2}`

. The graph of the function
passes through the point `(1, -3)`

. What is the equation of the function?

A. ```
\displaystyle
f(x) = 2x^2 -6x + 11
```

B. ```
\displaystyle
f(x) = 2x^2 +6x - 11
```

C. ```
\displaystyle
f(x) = 3x^2 - 2\sqrt{5}x - 4
```

D. ```
\displaystyle
f(x) = 2x^2 + 2\sqrt{5}x -3
```

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Q4

The sum, `S`

, and product, `P`

, of the roots of the function `f(x) = -3x^2 + 24x + 477`

are

A. S = 24, P = 477

B. S = 24, P = 1437

C. S = 8, P = -159

D. S = -8, P = 159

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Q5

If `x^y = 4`

, then the value of `x^{3y}-x^{2y}`

is

A. 48

B. 64

C. 4

D. 12

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Q6

If `M = 5^x + 5^{-x}`

and `N = 5^x =5^{-x}`

, then the value fo `M^2 -N^2`

is

A. `2(5^{2x})`

B. `2(5^{-2x})`

C. 4

D. 0

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Q7

In the given diagram, XY = X2 = 15 and YZ = 18. The value of `\sin Z`

is

A. ```
\displaystyle
\frac{3}{5}
```

B. ```
\displaystyle
\frac{4}{5}
```

C. ```
\displaystyle
\frac{4}{9}
```

D. ```
\displaystyle
\frac{4}{3}
```

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Q8

Explain why the minimum value of `(x - a)^2 + (x - b)^2`

occurs when `x = \frac{a + b}{2}`

. What is the minimum value.

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Q9