Question

Find the equation of the quadratic function determined from the graph above.

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Answer 1

y = (x-2)²/3 - 3

Explanation:

the vertex is at (2,-3), so the vertex form of the function is

y = A(x-2)²-3

where A is a constant to be found.

We see that when x=5, y=0, so substitute values to find A.

0 = A(5-2)² - 3

solve for A to get

A(3²) = 3

A = 1/3

So the equation is

y = (x-2)²/3 - 3

Check for x = -1

y = (-1-2)²/3 - 3 = 0 checks

Answer 2

Problem:-

Find the equation of the quadratic function determined from the graph above.

Solution:-

The vertex of the graph of the quadratic function is (2, -3). The graph passes through the point (5, 0). By replacing x and y with 5 and 0, respectively, and h and k with 2 and -3, respectively we have,

`\sf\rightarrow{y=a(x-h)²+k}`

`\sf\rightarrow{O=a(5-2)²-3}`

`\sf\rightarrow{0=a(3)²-3}`

`\sf\rightarrow{3=9a}`

`\sf\rightarrow{a=(1)/(3)}`

Answer:-

• Thus, the quadratic equation is...

`\sf\rightarrow{y=(1)/(3)(x-2)²-3}`

or,

`\sf{y=(1)/(3) \: x²-(4)/(3) \: x-(5)/(3)}`

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#Hope it helps!

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