Question

Write a quadratic function in standard form whose graph passes through (4,0) and (6,0)

Answer 1

Answer:

f(x) = x² - 10x + 24

Step-by-step explanation:

The quadratic function has a graph that passes through the points (4,0) and (6,0).

Therefore, the graph has two x-intercepts at x = 4 and x = 6 and those are the roots of the equation.

So, (x - 4) and (x - 6) are two factors of the quadratic equation.

Then we can write the equation as  

f(x) = (x - 4)(x - 6)

⇒ f(x) = x² - 4x - 6x + 24

⇒ f(x) = x² - 10x + 24

Hence, this is the required quadratic function in standard form. (Answer)