Question

what is the y-intercept of the function?
$f(x) = -0.2x^2 + 0.5x - 0.9$
the y-intercept is \boxed{}. (type an ordered pair, using integers or decimals.)

Explanation:

Step1: Recall the definition of y - intercept

The y - intercept of a function \(y = f(x)\) is the point where the graph of the function intersects the y - axis. On the y - axis, the x - coordinate is always \(0\). So, to find the y - intercept, we substitute \(x = 0\) into the function \(f(x)\).

Step2: Substitute \(x = 0\) into the function \(f(x)=- 0.2x^{2}+0.5x - 0.9\)

When \(x = 0\), we have:
\(f(0)=-0.2(0)^{2}+0.5(0)-0.9\)
First, calculate each term:

• For the term \(-0.2(0)^{2}\), since \(0^{2}=0\), then \(-0.2\times0 = 0\).
• For the term \(0.5(0)\), \(0.5\times0=0\).
• The last term is \(-0.9\).

So, \(f(0)=0 + 0-0.9=-0.9\).

Since the x - coordinate of the y - intercept is \(0\) and the y - coordinate is \(f(0)=-0.9\), the y - intercept is the ordered pair \((0,-0.9)\).

Answer:

\((0, - 0.9)\)