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3 years ago

62 decreased by twice Gail’s height let g represent Gail’s height

1 answer:

5 0

Answer:
62 - 2g

Explanation:
Before we begin, note the following:
a decreased by b means that we will subtract b from a, In other words, the expression would be a - b

Now, for our problem:
We have "g" is Gail's height.

The given information is as follows:
i. twice Gail's height means that we will multiply the height by 2. This will give us 2g
ii. 62 decreased by 2g means that we will subtract 2g from 62.

Based on the above, the expression would be:
62 - 2g

Hope this helps :)

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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:

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Solution :

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

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Applying middle term split,

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

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

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

$x=4,-3$

The x-intercepts are (4,0) and (-3,0).

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,

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4 years ago

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Data:
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