Question

for $f(x) = x^2 - 5x + 3$, what is the domain of the function?
o a. $(0,5)$
o b. $(0,3)$
o c. $1,\infty)$
o d. $(-\infty,\infty)$

the quadratic function $y = 5x^2 - 20x + 15$ opens upwards. what is its vertex?
o a. $(2,-5)$
o b. $(-2,-5)$
o c. $(-2,5)$
o d. $(2,5)$

Explanation:

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Problem 1: Domain of $f(x)=x^2-5x+3$

Step1: Identify function type

The function is a polynomial (quadratic).

Step2: Recall polynomial domain rule

All real numbers are valid inputs for polynomials.
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Problem 2: Vertex of $y=5x^2-20x+15$

Step1: Find x-coordinate of vertex

For $ax^2+bx+c$, use $x=-\frac{b}{2a}$.
$x=-\frac{-20}{2\times5}=\frac{20}{10}=2$

Step2: Find y-coordinate of vertex

Substitute $x=2$ into the function.
$y=5(2)^2-20(2)+15=5(4)-40+15=20-40+15=-5$

Answer:

1. d. $(-\infty, \infty)$
2. a. $(2, -5)$