Determining Correct Math Claims: Y-Intercept, X-Intercepts, and Vertex

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.

To determine which student’s claim about the function is correct, we can analyze each claim one by one:

Jeremiah claims that the y-intercept is at (15, 0)

To determine which student’s claim about the function is correct, we can analyze each claim one by one:

Jeremiah claims that the y-intercept is at (15, 0). To find the y-intercept, we set x = 0 and evaluate f(x):
f(0) = (0 + 3)(0 + 5) = 3 * 5 = 15
So, Jeremiah’s claim is incorrect. The y-intercept is (0, 15), not (15, 0).

Lindsay claims that the x-intercepts are at (-3, 0) and (5, 0). To find the x-intercepts, we set f(x) = 0 and solve for x:
(x + 3)(x + 5) = 0
Setting each factor equal to 0:
x + 3 = 0 -> x = -3
x + 5 = 0 -> x = -5
So, Lindsay’s claim is incorrect. The x-intercepts are at (-3, 0) and (-5, 0), not (-3, 0) and (5, 0).

Stephen claims that the vertex is at (-4, -1). To find the vertex of a quadratic function in the form f(x) = ax^2 + bx + c, the x-coordinate of the vertex is -b/(2a), and the y-coordinate is f(-b/(2a)). In this case, a = 1, b = 8, and c = 15.
x-coordinate of the vertex = -8/(2*1) = -4
y-coordinate of the vertex = f(-4) = (-4 + 3)(-4 + 5) = (-1)(1) = -1
So, Stephen’s claim that the vertex is at (-4, -1) is correct.

Alexis claims that the midpoint between the x-intercepts is at (4, 0). We can verify this by finding the average of the x-intercepts:
Average of x-intercepts = (-3 + 5) / 2 = 2 / 2 = 1
So, Alexis’ claim is incorrect. The midpoint between the x-intercepts is (1, 0), not (4, 0).

Therefore, the correct claim is Stephen’s, who states that the vertex is at (-4, -1).

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