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Katena32 [7]
3 years ago
11

Write an equation of the parabola in vertex form

Mathematics
1 answer:
soldi70 [24.7K]3 years ago
4 0

Step-by-step explanation:

Recall that a parabola is the graph representing a quadratic equation, which is standard form is as follows:

y = ax2 + bx + c

where the value of 'a' determines whether the parabola opens upwards of downwards (i.e., the parabola opens upwards if a>0 and opens downwards if a<0) and the axis of symmetry is given by the line x = -b/(2a).

The vertex form of a parabola's (or a quadratic) equations is given by the following formula:

y = a(x - h)2 + k , where (h, k) is the vertex and the axis of symmetry is given by the line x = h.

Given that the vertex is at (0, 3), then ..... h = 0 and k = 3 ..... thus,

y = a(x - 0)2 + 3

y = a(x)2 + 3

With a point at (-4, -45), then ..... x = -4 and y = -45 ..... therefore,

-45 = a(-4)2 + 3

-45 = a(16) + 3

Solve for a by first subtracting 3 from both sides of the equation then dividing both sides of the equation by 16:

-45 - 3 = a(16) + 3 - 3

-48 = a(16)

-48/16 = 16a/16

-3 = a

With a vertex (h, k) at (0, 3) and given that a = -3, then the equation of this parabola in vertex form is as follows:

y = a(x - h)2 + k

y = -3(x - 0)2 + 3

y = -3x2 + 3

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A parabola whose equation is y = (x - 5)^2 - 2 has a vertex at _____.
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The vertex would be at (5,-2)
7 0
3 years ago
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What is the equation of the line that passes through the point (−1,−3) and has a slope of 3?
Tanya [424]

Answer:

y= 3x

Step-by-step explanation:

The slope is just read. It is 3. It is the value of m in the general equation.

y = mx + b

y = 3x + b

To find b, use (-1,-3)

x = -1

y = -3                  Substitute into the general equation

-3 = 3(-1) + b       Simplify the right side

-3 = -3 + b          Subtract -3 from both sides

b = 0

Answer: y = 3x

7 0
2 years ago
Mr. Nelson bought a car for $20,000 with a 5% interest rate.
LekaFEV [45]

Answer:

A ) Hence The interest for the car loan is $ 4,310

B ) Hence The interest for the car loan is $ 3,152

Step-by-step explanation:

Given as :

The loan for the car = $ 20,000

The rate of interest of car loan = 5 % compounded annually

A ) The period of loan = 48 months = 4 years

Let the interest of the loan = CI

<u>From compounded method</u>

Amount = Principal × (1 + \frac{\textrm Rate}{100})^{\textrm time}

Or, Amount = $ 20,000 × (1 + \frac{\textrm 5}{100})^{\textrm 4}

Or,  Amount = $ 20,000 × (1.05)^{4}

Or, Amount = $ 20,000 × 1.2155

∴ Amount = $ 24310

So, Interest = Amount - Principal

Or, CI = $ 24,310 - $ 20,000  

∴  CI = $ 4,310

Hence The interest for the car loan is $ 4,310

B ) The loan for the car = $ 20,000

The rate of interest of car loan = 5 % compounded annually

The period of loan = 3 years

Let the interest of the loan = CI

So,

<u>From compounded method</u>

Amount = Principal × (1 + \frac{\textrm Rate}{100})^{\textrm time}

Or, Amount = $ 20,000 × (1 + \frac{\textrm 5}{100})^{\textrm 3}

Or,  Amount = $ 20,000 × (1.05)^{3}

Or, Amount = $ 20,000 × 1.1576

∴ Amount = $ 23,152

So, Interest = Amount - Principal

Or, CI = $ 23,152 - $ 20,000  

∴  CI = $ 3,152

Hence The interest for the car loan is $ 3,152

6 0
3 years ago
Please answer the question step by step!
erma4kov [3.2K]

Answer:

Step-by-step explanation:

See the figure below.

This is how you graph directly from the equation in the slope-intercept form (y = mx + b) without having to create a table of x and y values.

The equation is

y = -2/3 x + 1

Compare it with

y = mx + b

b = 1

The y-intercept is 1, so mark 1 on the y-axis. (You already did.)

I placed a black dot there.

The slope is m.

m = -2/3

slope = m = rise/run

A slope of -2/3 can be though of as -2 rise and 3 run. That means start from the y-intercept, and go -2 in y (a rise of 2 down) and 3 in x (a run 3 right). Point graphed in red.

Mathematically, -2/3 is the same as 2/(-3), so starting again from the y-intercept, this slope can also be though of as rise of 2 in y (a rise of 2 up) and a run of -3 in x (a run of 3 left). Point graphed in green.

The line is graphed in blue.

5 0
2 years ago
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