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3 years ago

Vertex (-3,7) point:(-2,,-5)

Mathematics

1 answer:

Vladimir79 [104]3 years ago

7 0

Answer:

y= -12x^2 -72x + 101(standard form)

y= -12(x+3)^2+7(vertex form)

Step-by-step explanation:

Standard form : y=ax^2 + bx + c

Using the vertex(h,k) we can find the vertex form of the equation which is:

y = a(x-h)^2+k

y=a(x+3)^2+7

Because we have a point we can use that to find the slope:

-5=a(-2+3)^2+7

-5=a(1)^2+7

-5-7=a

a=-12

So, in standard form:

y=-12(x+3)^2+7

y=-12(x^2+6x+9)+7

y= -12x^2 -72x -108+7

y= -12x^2 -72x- 101

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Answer:

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Step-by-step explanation:

use the Pythagorean theorem

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3 years ago

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zhannawk [14.2K]

Answer:

y= -2x+2.

Step-by-step explanation:

1) according to the condition interception is '2' (point (0;2));

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2 years ago

The graph of a quadratic function having the form f(x) = ax? + bx + c passes

insens350 [35]

Answer:

f(-3) = -20

Step-by-step explanation:

We observe that the given x-values are 3 units apart, and that the x-value we're concerned with is also 3 units from the first of those given. So, a simple way to work this is to consider the sequence for x = 6, 3, 0, -3. The corresponding sequence of f(x) values is ...

34, 10, -8, ?

The first differences of these numbers are ...

10 -34 = -24

-8 -10 = -18

And the second difference is ...

-18 -(-24) = 6

For a quadratic function, second differences are constant. This means the next first-difference will be ...

? -(-8) = -18 +6

? = -12 -8 = -20

The value of the function at x=-3 is -20.

_____

The attachment shows using a graphing calculator to do a quadratic regression on the given points. The graph can then be used to find the point of interest. There are algebraic ways to do this, too, but they are somewhat more complicated than the 5 addition/subtraction operations we needed to find the solution. (Had the required x-value been different, we might have chosen a different approach.)