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sukhopar [10]
3 years ago
10

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of y=4x^2+5x-1

Mathematics
1 answer:
Ivanshal [37]3 years ago
4 0
Answer:

Axis of symmetry: x=-\frac{5}{8}

Vertex: (-\frac{5}{8},-2\frac{9}{16})

Step-by-step explanation:

The given quadratic equation is

y=4x^2+5x-1

By comparing to the general quadratic function; y=ax^2+bx+c

We have a=4,b=5,c=-1

The equation of the axis of symmetry is given by the formula;

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

We got this formula by completing the square on the general quadratic function.

We substitute a=4 and b=5 to obtain;

x=-\frac{5}{2(4)}

x=-\frac{5}{8}
is the axis of symmetry.

To find the y-value of the vertex, we put x=-\frac{5}{8} into the function to obtain;

y=4(-\frac{5}{8})^2+5(-\frac{5}{8})-1

y=4(-\frac{5}{8})^2+5(-\frac{5}{8})-1

y=-\frac{41}{16}

The vertex of the given function is (-\frac{5}{8},-2\frac{9}{16})
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Help please Which is the equation of a trend line that passes through the points (3, 95) and (11, 12)? Round values to the neare
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An apartment complex has a floor plan with dimensions shown. To effectively air condition a room, 20 BTU’s are required for ever
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12,900 BTU's are required to cool the room effectively.

Step-by-step explanation:

Step 1:

We must calculate the area of the entire shape to determine the minimum BTU's required to cool the room effectively.

It is made up of a semi-circle a rectangle, and a trapezoid.

Step 2:

The area of a semi-circle =\frac{ \pi r^{2} }{2} .

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The area of the semi-circle =\frac{ \pi r^{2} }{2} =\frac{ (\pi) (10^{2}) }{2} = 157.079 square feet.

The area of a rectangle = (l)(w).

The length of the rectangle is 22 feet and the width is 20 feet.

The area of a rectangle = (l)(w) =(22)(20) = 440 square feet.

The area of a trapezoid =\frac{a+b}{2} (h).

Here a=12, b= 20, h= 3.

The area of a trapezoid =\frac{12+20}{2} (3) = 48 square feet.

Step 3:

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The number of BTU's for 645.079 square feet = (645.079)(20)=12,901.58 BTU's.

Rounding this off, we get 12,900 BTU's required  to cool the room effectively.

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