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RUDIKE [14]
3 years ago
15

What is the equation of the following graph in vertex form?

Mathematics
1 answer:
Veronika [31]3 years ago
5 0

Answer:

The equation in vertex form is:

y=(x-2)^2+1

Step-by-step explanation:

Recall that the formula of a parabola with vertex at (x_{vertex},y_{vertex}) is given by the equation in vertex form:

y=a\,(x-x_{vertex})^2+y_{vertex}

where the parameter "a" can be specified by an extra information on any other point apart from the vertex, that parabola goes through.

In our case, since the vertex must be the point (2, 1), the vertex form of the parabola becomes:

y=a\,(x-x_{vertex})^2+y_{vertex}\\y=a\,(x-2)^2+1

we have the information on the extra point (0, 5) where the parabola crosses the y-axis. Then, we use it to find the missing parameter a:

y=a\,(x-2)^2+1\\5=a(0-2)^2+1\\5=a\,*\,4+1\\5-1=4\,a\\4=4\,a\\a=1

The, the final form of the parabola's equation in vertex form is:

y=(x-2)^2+1

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Step-by-step explanation:

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3 years ago
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<h3>What are percentages?</h3>

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6 0
2 years ago
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Step-by-step explanation:

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3 years ago
14 divided by 3/8 ? (The question mark is not part of the problem...neither is this..)
dmitriy555 [2]
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4 0
3 years ago
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Please help, thank you
madam [21]

Answer:

\displaystyle x=\frac{-8\pm\sqrt{(8)^2-4(4)(-221)}}{2(4)}\ \text{; x = 6.5 and x = -8.5}

Step-by-step explanation:

Subtract the right side of the given equation to put it into standard form:

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Then the coefficients used in the quadratic formula are ...

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When these are filled into the form ...

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7 0
3 years ago
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