Question

write a quadratic function in standard form whose graph is shown. the function is $f(x)=square$.

Explanation:

Step1: Write factored form

Since the x - intercepts are $x = 3$ and $x = 5$, the factored form of the quadratic function is $y=a(x - 3)(x - 5)$.

Step2: Find the value of a

Substitute the point $(6,-3)$ into $y=a(x - 3)(x - 5)$. We get $-3=a(6 - 3)(6 - 5)$. Simplify the right - hand side: $-3=a\times3\times1$, so $a=-1$.

Step3: Convert to standard form

Expand $y=-(x - 3)(x - 5)=-(x^{2}-5x-3x + 15)=-x^{2}+8x - 15$.

Answer:

$-x^{2}+8x - 15$