Questions: For each function, f(x) and g(x), what should the constant term of the equation be for each function? Give a reason for your answer. What would the factors of f(x) be? Give a reason for your answer. What would the equation of f(x) be in standard form? Show your work What would the factors of g(x) be? Give a reason for your answer. What would the equation of f(x) be in standard form? Show your work

For each function, f(x) and g(x), what should the constant term of the equation be for each function? Give a reason for your answer.

What would the factors of f(x) be? Give a reason for your answer.

What would the equation of f(x) be in standard form? Show your work

What would the factors of g(x) be? Give a reason for your answer.

What would the equation of f(x) be in standard form? Show your work

Transcript text: For each function, $f(x)$ and $g(x)$, what should the constant term of the equation be for each function? Give a reason for your answer. What would the factors of $f(x)$ be? Give a reason for your answer. What would the equation of $f(x)$ be in standard form? Show your work What would the factors of $g(x)$ be? Give a reason for your answer. What would the equation of $f(x)$ be in standard form? Show your work

Solution

Solution Steps

Step 1: Finding the constant term

The constant term of a quadratic function corresponds to the y-intercept of its graph. For f(x), the graph intersects the y-axis at -5. For g(x), the graph intersects the y-axis at -4.

Step 2: Finding the factors of f(x)

The graph of f(x) intersects the x-axis at x = -1 and x = 5. Therefore, the factors are (x + 1) and (x - 5).

Step 3: Finding the equation of f(x) in standard form

We multiply the factors of f(x) together and adjust the constant to match the y-intercept we found: (x+1)(x-5) = x² - 5x + x - 5 = x² - 4x - 5. Since the graph shows the y-intercept to be at y = -5, the equation remains x²-4x-5.