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What is the y-intercept of the quadratic function f(x) = (x – 8)(x + 3)? (8,0) (0,3) (0,–24) (–5,0)

2 Answers

3 votes

The first step that we must take to solve a problem is to understand that the problem statement is asking us to do and what is given to us to do so. Looking at the problem statement we can see that they are asking us to determine what the y-intercept of the quadratic function is. We are given the expression
f(x) = (x - 8)(x + 3) to help us accomplish that goal.

After completing that step, we can move onto the next step which is actually determining what the y-intercept is. We know that the y-axis is when x = 0 so therefore if we set x to 0 in the expression provided we will be able to solve for the unknown. The unknown will then lead us to the y-intercept. One more thing that I needed to state was that f(x) is almost the same exact thing as y but just in a different format.

Plug in 0 for all of the x values


  • f(x) = (x - 8)(x + 3)

  • f(x) = (0 - 8)(0 + 3)

Simplify the expression


  • f(x) = (- 8)(3)

  • f(x) = -24

Looking at the value that we got from the equation we can see that f(x) or y is equal to -24 when x is equal to 0. This would in turn give us the coordinate of (0, -24) where the first digit corresponds to the x-value and the second digit corresponds to the y-value.

Therefore, the option that would make the most sense would be option C, (0, -24)

User Aswani Madhavan
by
4.4k points
4 votes

The correct answer is: [C]: " (0, - 24) " .
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Step-by-step explanation:
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Given the function:

" y = (x − 8) (x + 3) " ; ← Note: Replace the "f(x)" with: "y" ;

→ Find the "y-intercept".

Note: The "y-intercept" is the coordinate of the point(s) of the graph of the equation at which the graph crosses the "x-axis" when "x = 0" .
So; we plug in "0" for "x" into our equation; & then: solve for "y" ;

→ " y = (x − 8) (x + 3) " ;

→ y = (0 − 8) (0 + 3) ;

y = (-8) * (3) ;

→ " y = - 24 " .
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→ which corresponds to: Answer choice: [C]: " (0, - 24) " .
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Hope this is helpful to you! Wishing you well!
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User Theadnangondal
by
5.4k points
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