Questions: What is the correct quadratic function for this parabola? a. f(x)=(x-2)(x-3) b. f(x)=(x+2)(x-3) c. f(x)=(x-2)(x+3) d. f(x)=(x+2)(x+3)

What is the correct quadratic function for this parabola? a. f(x)=(x-2)(x-3) b. f(x)=(x+2)(x-3) c. f(x)=(x-2)(x+3) d. f(x)=(x+2)(x+3)
Transcript text: 9. What is the correct quadratic function for this parabola? a. $f(x)=(x-2)(x-3)$ b. $f(x)=(x+2)(x-3)$ c. $f(x)=(x-2)(x+3)$ d. $f(x)=(x+2)(x+3)$
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Solution

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Solution Steps

Step 1: Find the x-intercepts

The graph crosses the x-axis at x = -3 and x = 2. These are the roots of the quadratic equation.

Step 2: Determine the factors

Since the roots are -3 and 2, the factors of the quadratic function are (x+3) and (x-2).

Step 3: Write the quadratic function

The quadratic function can be written as f(x) = (x+3)(x-2) which is the same as f(x) = (x-2)(x+3).

Final Answer

c. $f(x) = (x-2)(x+3)$

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