Question

Doran wants to graph g(x) = 4x^2 - 24x + 7. He ends up with the graph shown. What mistake did Doran make, and what result should he have gotten?

a) Doran miscalculated the vertex and should have obtained a vertex of (-3, 115).
b) Doran correctly calculated the vertex, which should be (-3, 115).
c) Doran correctly calculated the vertex, which should be (3, -115).
d) Doran miscalculated the y-intercept and should have obtained a y-intercept of (0, 7).

Answer 1

Doran made a mistake in calculating the y-intercept of the quadratic function g(x) = 4x^2 - 24x + 7. The correct y-intercept should be (0, 7), and Doran should have graphed this point as part of the equation. Consequently, the correct choice is option (d), indicating a miscalculation of the y-intercept.

Step-by-step explanation:

The question refers to the function g(x) = 4x2 - 24x + 7, which is a quadratic equation in standard form. Doran's task is to graph this function, which would involve finding key features such as the vertex and the y-intercept. To find the vertex of a quadratic function in standard form, g(x) = ax2 + bx + c, we use the formula -b/(2a) for the x-coordinate of the vertex. Here, a = 4 and b = -24, so the x-coordinate of the vertex would be -(-24)/(2*4) = 3. Plugging this back into the function yields the vertex as (3, -115) since g(3) = 4(3)2 - 24*3 + 7.

The y-intercept occurs when x=0, so for the given function, the y-intercept would be g(0) = 7, which is point (0, 7) on the graph. Therefore, the correct result Doran should have obtained is option (d), which indicates that Doran may have miscalculated the y-intercept and should have obtained a y-intercept of (0, 7).