Describe the key features of the graph of the quadratic function f(x) = x2 - 8x - 20

1 answer:

7 0

If f(x)=x^2-8x-20 then

dy/dx=2x-8 and d2y/dx2=2

A) Since acceleration is a constant positive the parabola opens upward.

B) Since acceleration is a constant positive the parabola will have a vertex at an absolute minimum

C) The vertex will occur when dy/dx=0, 2x-8=0, 2x=8, x=4

So the axis of symmetry is the vertical line x=4.

The vertex is y(4)=-36, corresponding to the vertex point (4,-36)

The y-intercept occurs when x=0, y(0)=-20, so the y-intercept is the point (0,-20)

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Fiona and Pip win some money and share it in the ratio 6:1. Fiona gets £35 more than Pip. How much did they get altogether?

Softa [21]

$\boxed{ \mathfrak { question↷}}$

Fiona and Pip win some money and share it in the ratio 6:1. Fiona gets £35 more than Pip. How much did they get altogether?

$\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}$

$\boxed{ \mathfrak { solution↷}}$

Let Pip get be x and fiona get be x+35

Ratio = 6:1

$\tt \frac{x + 35}{x } = 6$

$\tt \: x + 35 = 6x$

$\tt \: 5x = 35$

$\tt \: x = 7$

$\boxed{ \sf \: Total \: money = x + x + 35 = 14+ 35 = £49}$

3 0

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An assistant cook peeled 18 potatoes in 6 minutes. At this rate, how many potatoes can he peel in 50 minutes?

malfutka [58]

Answer:

$150$ potatoes

Step-by-step explanation:

Since the assistant can peel $18$ potatoes in $6$ minutes, we know that he can peel $\frac{18}{6}=3$ potatoes in $1$ minute. Therefore, he will be able to peel $3*50=150$ potatoes in $50$ minutes. Hope this helps!