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yulyashka [42]
3 years ago
6

Frank is playing a game where he loses 1.5 points every time a critter eats a carrot. After two rounds of hte game, he lost 13.5

points. Which equation represents the number of carrots the critter ate?
Mathematics
1 answer:
Tpy6a [65]3 years ago
8 0

Answer:9

Step-by-step explanation: 13.5/1.5=9

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Consider the quadratic function f(x) = -x^2 + 1x + 12. Determine the following: (enter all numerical answers as integers, fracti
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Answer and Explanation:

Given : The quadratic function f(x)=-x^2+x+12

To find : Determine the following ?

Solution :

The x -intercept are where f(x)=0,

So, -x^2+x+12=0

Applying middle term split,

-x^2+4x-3x+12=0

-x(x-4)-3(x-4)=0

(x-4)(-x-3)=0

x=4,-3

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The smallest x-intercept is x=-3

The largest x-intercept is x=4

The y -intercept are where x=0,

So, f(0)=-(0)^2+0+12

f(0)=12

The y-intercept is y=12.

The quadratic function is in the form, y=ax^2+bx+c

On comparing, a=-1 , b=1 and c=1 2

The vertex of the graph is denote by (h,k) and the formula to find the vertex is

For h, The x-coordinate of the vertex is given by,

h=-\frac{b}{2a}

h=-\frac{1}{2(-1)}

h=\frac{1}{2}

For k, The y-coordinate of the vertex is given by,

k=f(h)

k=-h^2+h+12

k=-(\frac{1}{2})^2+\frac{1}{2}+12

k=-\frac{1}{4}+\frac{1}{2}+12

k=\frac{-1+2+48}{4}

k=\frac{49}{4}

The vertex of the function is (h,k)=(\frac{1}{2},\frac{49}{4})

The x-coordinate of the vertex i.e. x=-\frac{b}{2a} is the axis of symmetry,

So, x=-\frac{b}{2a}=\frac{1}{2} (solved above)

The axis of symmetry is x=\frac{1}{2}.

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