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ollegr [7]
2 years ago
14

The graph of quadric function has a minumum at (-2,-3) and passes through the point (2,13)

Mathematics
1 answer:
Leto [7]2 years ago
3 0

Answer:

g(x) = x² + 4x + 1

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (- 2, - 3), thus

y = a(x + 2)² - 3

To find a substitute (2, 13) into the equation

13 = a(2 + 2)² - 3

13 = 16a - 3 ( add 3 to both sides )

16 = 16a ( divide both sides by 16 )

a = 1, hence

g(x) = (x + 2)² - 3 ← expand factor and simplify

      = x² + 4x + 4 - 3

g(x) = x² + 4x + 1

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Answer:

y = -1/4x + 3

Step-by-step explanation:

y=mx+b is the slope-intercept form, which your equation y=4x-4 is already in.

To find the perpendicular line, you must take the <u>negative reciprocal</u> of the slope.

y = -1/4x + b

Your "b" will not be the same as the given equation, since the y-intercepts will not be the same. Therefore, you must solve for it using the point given.

Plug in (4, 2) [general: (x, y)] to the corresponding spots in y = -1/4x + b.

(2) = -1/4(4) + b

2 = -1 + b

b = 3

Now that you know m and b, you can plug all the values back into the form y = mx+b.

**Remember that y and x are never plugged back in! You need two variables to have a linear line

y = -1/4x + 3 is the answer.

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Which equation represents the line that is perpendicular to graph of 4x+3y=9 and passes through (-2,3)
goldfiish [28.3K]

4y = 3x + 18

Step-by-step explanation:

NOTE THAT A line that is perpendicular to another has a negative inverse of the slope of the other line. The products of their slopes, that is, is always -1

Therefore we can begin by finding the slope of this line defined by the function 4x+3y=9

3y = -4x + 9

y = -4/3 x + 9/3

y = -4/3 x + 3

The slope of the  perpendicular line is, therefore;

¾  - this is the negative inverse of -4/3

Now that we know the slope, we need to find the y-intercept. This is where x = 0 and the line meets the y-axis;

i.e (0, y)

The other given point, where the line crosses  is (-2, 3). Remember that to get the gradient we use the formula;

Gradient = Δ y / Δ x

¾ = (3 – y) / (-2 – 0)

¾ = (3 –y) / -2  

¾ * -2 = 3 – y

-3/2 = 3 – y

-3/2 – 3 = -y

9/2 = y           ←– This is the y-intercept

Remember the function of a straight line is given;

y = mx + c (m being slope and c being y-intercept)

y = 3/4 x + 9/2

4y = 3x + 18

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