Mr. Walker gave his class the function f(x) = (x + 3)(x + 5). Four students made a claim about the function. Each student’s claim is below.Jeremiah: The y-intercept is at (15, 0).Lindsay: The x-intercepts are at (-3, 0) and (5, 0).Stephen: The vertex is at (-4, -1).Alexis: The midpoint between the x-intercepts is at (4, 0).Which student’s claim about the function is correct?The claim by is correct.
Stephen
Lindsay’s claim is correct.
To find the y-intercept, we set x = 0 in the function:
f(0) = (0 + 3)(0 + 5) = 15
So the y-intercept is at (0, 15), not (15, 0) as Jeremiah claimed.
To find the x-intercepts, we set y = 0 in the function:
0 = (x + 3)(x + 5)
Solving for x, we get x = -3 and x = -5. So the x-intercepts are at (-3, 0) and (-5, 0), not at (5, 0) as Jeremiah claimed.
To find the vertex, we can complete the square:
f(x) = (x^2 + 8x + 15) – 6
f(x) = (x + 4)^2 – 1
So the vertex is at (-4, -1), which confirms Stephen’s claim.
To find the midpoint between the x-intercepts, we take the average of the x-coordinates:
(5 + (-3))/2 = 1
So the midpoint is at (1, 0), not (4, 0) as Alexis claimed.
Therefore, only Lindsay’s claim about the x-intercepts is correct.
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