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,
[tex]\sf\rightarrow{y=a(x-h)²+k}[/tex]
[tex]\sf\rightarrow{O=a(5-2)²-3}[/tex]
[tex]\sf\rightarrow{0=a(3)²-3}[/tex]
[tex]\sf\rightarrow{3=9a}[/tex]
[tex]\sf\rightarrow{a=\frac{1}{3}}[/tex]
Answer:-
- Thus, the quadratic equation is...
[tex]\sf\rightarrow{y=\frac{1}{3}(x-2)²-3}[/tex]
or,
[tex]\sf{y=\frac{1}{3} \: x²-\frac{4}{3} \: x-\frac{5}{3}}[/tex]
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#Hope it helps!
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