Consider the graph of the equation y=ax^2+bx+c, when a does not equal 0. If a is multiplied by 3, what is true of the graph of the resulting parabola?
(A) The Vertex is 3 units above the vertex of the original.
(B) The new parabola is wider than the original.
(C) The new parabola is 3 units to the right of the original.
(D) The new parabolais narrowerthan the original.
|y| is bigger for every big x so parabola is narrower
whats the answer
If we multiply the coefficient "a" in the equation y = ax^2 + bx + c by 3, the resulting equation becomes y = 3ax^2 + bx + c.
To determine the effects on the graph, we consider the standard form of a parabola, which is y = a(x-h)^2 + k, where (h,k) represents the vertex of the parabola.
Comparing the original equation y = ax^2 + bx + c with the new equation y = 3ax^2 + bx + c, we can see that the only change is the coefficient in front of x^2.
Therefore, we can deduce that the new parabola (y = 3ax^2 + bx + c) will be wider or narrower than the original parabola depending on whether a (the coefficient in front of x^2) is greater than or less than 1.
Since the question specifically mentions that a does not equal 0, we know that the coefficient a is non-zero.
Therefore, the correct answer to the question is:
(D) The new parabola is narrower than the original.
To determine the effect of multiplying the coefficient "a" by 3 in the equation y = ax^2 + bx + c, we need to understand how it impacts the shape and position of the graphed parabola.
The standard form of a quadratic equation is y = ax^2 + bx + c, where "a" represents the coefficient of x^2, "b" represents the coefficient of x, and "c" is a constant term.
In this case, multiplying "a" by 3 changes the coefficient that affects the shape of the parabola. Let's analyze the given options one by one to find the correct answer:
(A) The vertex is not directly influenced by multiplying "a" by 3. Therefore, option (A) is incorrect.
(B) Multiplying "a" by 3 actually makes the parabola narrower, not wider. When "a" is multiplied by a positive number greater than 1, it compresses the parabola vertically, making it narrower. Therefore, option (B) is incorrect.
(C) Multiplying "a" by 3 does not impact the horizontal positioning of the parabola. The position of the parabola or the vertex is determined by the coefficients "b" and "c," not "a." Therefore, option (C) is incorrect.
(D) As mentioned earlier, multiplying "a" by 3 results in a narrower parabola. Therefore, option (D) is the correct answer.
To summarize, when the coefficient "a" in the equation y = ax^2 + bx + c is multiplied by 3, the resulting parabola will be narrower than the original.