Final answer:
To find the equation of the quadratic function in standard form with given roots and a point on the graph, we can use the fact that the roots are also the x-intercepts. By using the roots of 4 and 1, we can find the factors of the quadratic function. Multiplying these factors and plugging in the given point (-3, -7), we find that the equation is f(x) = (x-4)(x-1), which corresponds to option A.
Step-by-step explanation:
To find the equation of a quadratic function in standard form given the roots and a point on the graph, we can use the fact that the roots of a quadratic function are also the x-intercepts of its graph. We start by using the given roots, 4 and 1, to find the factors of the quadratic function. The factors are (x-4) and (x-1). To find the equation, we can multiply these factors together and use the given point (-3, -7) to determine the value of the leading coefficient.
Plugging in the coordinates of the given point, we get (-7) = a((-3)-4)((-3)-1), which simplifies to (-7) = a(-7)(-4). Solving for a, we find that a = 1.
Therefore, the equation of the quadratic function in standard form is f(x) = (x-4)(x-1), which corresponds to option A.