Question

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

Answer 1

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,

$\sf\rightarrow{y=a(x-h)²+k}$

$\sf\rightarrow{O=a(5-2)²-3}$

$\sf\rightarrow{0=a(3)²-3}$

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

$\sf\rightarrow{a=\frac{1}{3}}$

Answer:-

• Thus, the quadratic equation is...

$\sf\rightarrow{y=\frac{1}{3}(x-2)²-3}$

or,

$\sf{y=\frac{1}{3} \: x²-\frac{4}{3} \: x-\frac{5}{3}}$

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Answer 2

Answer:

y = (x-2)²/3 - 3

Step-by-step 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