Question

# The factored form of a quadratic function is f(x)=(x‒p)(x‒q).

The factored form of a quadratic function is $$f(x)=(x‒p)(x‒q)$$. The standard form of a quadratic function is $$\displaystyle{f{{\left({x}\right)}}}={a}{x}^{{2}}+{b}{x}+{c}$$. The factored form for a quadratic function tells us the x-intercepts of the quadratic function, while the standard form for a quadratic function tells us the y-intercept of the quadratic function.
If $$p=2$$ and $$q=-3$$, use what you have learned about multiplying polynomials to
- write the factored form of the quadratic function f(x)
- write the standard form for the quadratic function f(x)

2021-02-04

Factored form of the quadratic function f(x) is
$$f(x)=(x-p)(x-q)$$
put $$p=2, q=-3$$
$$=(x-2)(x-(-3))$$
$$f(x)=(x-2)(x+3))$$
Standart form of a quadraticfunction is $$f(x)=(x-2)(x+3)$$
$$\displaystyle={x}{\left({x}+{3}\right)}-{2}{\left({x}+{3}\right)}$$
$$\displaystyle={x}^{{2}}+{3}{x}-{2}{x}-{6}$$
$$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}+{x}-{6}$$