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Art [367]
3 years ago
10

What is the value of h when the function is converted to vertex form?

Mathematics
1 answer:
tatuchka [14]3 years ago
5 0
Y = x^2-14x+29
a = 1, b=14, c =29

h = b/2a
h = 14 / 2*1 = 14/2 = 7
 h = 7
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-8(5b + 2) -7(b - 5)
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-47b + 19

Step-by-step explanation:

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Two sidewalks in a park are represented by lines on a coordinate grid. Two points on each of the lines are shown in the tables.
algol [13]

Answer:

y = 2x + 1 ;

y - 3 = - 3(x - 1) ; y = - 3x + 6 ;

Independent ;

(1, 3)

Step-by-step explanation:

Given the data:

Sidewalk 1:

x __ y

2 _ 5

0 _ 1

Sidewalk 2:

x __ y

1 _ 3

3 _ -3

Equation for sidewalk 1 in slope - intercept form:

Slope intercept form:

y = mx + c

c = intercept ; m = slope

m = (change in y / change in x)

m = (1 - 5) / (0 - 2) = - 4 / - 2 = 2

Y intercept ; value of y when x = 0

(0, 1) ; y = 1

Hence, c = 1

y = 2x + 1

Sidewalk 2:

Point slope form:

y - y1 = m(x - x1)

m = slope

m = = (-3 - 3) / (3 - 1) = - 6/2 = - 3

Point (x1, y1) = (1, 3)

y - 3 = - 3(x - 1)

To slope intercept form:

y - 3 = - 3(x - 1)

y - 3 = - 3x + 3

y = - 3x + 3 + 3

y = - 3x + 6

Since the slope of both lines are different, intersection will be at single point and will have a single solution. This makes it independent.

Using substitution method :

y = 2x + 1 - - - (1)

y = - 3x + 6 - - - (2)

Substitute (1) into (2)

2x + 1 = - 3x + 6

2x + 3x = 6 - 1

5x = 5

x = 1

From (1)

y = 2(1) + 1

y = 2 + 1

y = 3

Coordinate of the point of intersection = (1, 3)

5 0
3 years ago
Graph the quadratic functions y = -2x^2 and y = -2x^2 + 4 on a separate piece of paper. Using those graphs, compare and contrast
kirza4 [7]

Answer:

They are represented by downward parabola

They have the same equations of line of symmetry

Their vertices have same x-coordinates but different y-coordinates

They have the same domains

They have different ranges

They have different maximum values at same x values

The graph of y = -2x² + 4 is the image of the graph y = -2x² after translation 4 units up

Step-by-step explanation:

y = -2x² is a quadratic equation which represents by a parabola

From the red graph:

The graph of y = -2x² is represented by downward parabola

It has a maximum vertex (0 , 0)

The line of symmetry at x = 0

Its maximum value = 0 at x = 0

Its domain is {x: x ∈ R}

Its range is {y: y ≤ 0}

From the blue graph:

The graph of y = -2x² + 4 is represented by down ward parabola

It has a maximum vertex (0 , 4)

The line of symmetry at x = 0

Its maximum value = 4 at x = 0

Its domain is {x: x ∈ R}

Its range is {y: y ≤ 4}

From the two graphs

They are represented by downward parabola

They have the same equations of line of symmetry

Their vertices have same x-coordinates but different y-coordinates

They have same domains

They have different ranges

They have different maximum values at same x values

The graph of y = -2x² + 4 is the image of the graph y = -2x² after translation 4 units up

8 0
4 years ago
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