the equation is f(x)=a(a-p)^2+q. Which statment is true?
A. a is less than zero because the graph opens upwards a q is zero because there are 2 x-intercepts
B. a is greater than zero because the graph opens upwards a q is zero because there are 2 x intercepts
C. the values a and q have opposite signs because there is 2 xintercepts
D. the values a and q have the same sign because there is 2 xintercepts.
I chose B, is that correct?
no one said anything about which way the graph opens.
Actually, without looking at the graph, there is no way to answer the question.
But, if there are 2 roots, then for sure C is correct, because
if it opens up, then the vertex is below the x-axis
if it opens down, then the vertex is above the x-axis.
Ya. Also I'm going on a break so cya everyone ill be back in a few minutes to check on your answers 😆😊💖🧡💛💚💙💜 (btw I'm just a kid I'm in 6th grade but I'm really smart I have all a's in my class almost all 100's so yeah :3)
I know nobody asked but I'm just saying C:
To determine which statement is true, we need to analyze the given equation f(x) = a(a-p)^2 + q, specifically examining the value of "a" and the number of x-intercepts.
The equation f(x) represents a quadratic function in the form of f(x) = ax^2 + bx + c, where "a" is the coefficient of the x^2 term, "b" is the coefficient of the x term, and "c" is the constant term.
In our given equation, f(x) = a(a-p)^2 + q, we can see that "a" is multiplied by the square of the expression (a-p) and added to the constant term q. By observing the equation, we can make the following conclusions:
1. The sign of "a":
- If "a" is positive, the graph of the quadratic function will open upwards (concave up).
- If "a" is negative, the graph will open downwards (concave down).
2. The number of x-intercepts:
- For a quadratic function in the form f(x) = ax^2 + bx + c, the number of x-intercepts is determined by the discriminant, which is given by b^2 - 4ac. If the discriminant is positive, there are two distinct x-intercepts. If it is zero, there is one repeated x-intercept (when the quadratic touches the x-axis but does not cross). And if it is negative, there are no x-intercepts.
Now, let's verify each of the statements:
A. "a is less than zero because the graph opens upwards and q is zero because there are 2 x-intercepts."
Based on the given equation f(x) = a(a-p)^2 + q, we cannot conclude that q is zero nor that a is less than zero solely based on the number of x-intercepts. Therefore, statement A is incorrect.
B. "a is greater than zero because the graph opens upwards and q is zero because there are 2 x-intercepts."
This statement correctly identifies that the graph opens upwards if "a" is greater than zero but is incorrect regarding the number of x-intercepts. Hence, statement B is also incorrect.
C. "The values a and q have opposite signs because there are 2 x-intercepts."
As mentioned earlier, the number of x-intercepts does not determine the sign of "a" or "q." We cannot infer their signs based on this information alone. Consequently, statement C is incorrect.
D. "The values a and q have the same sign because there are 2 x-intercepts."
Again, the number of x-intercepts does not provide any information about the signs of "a" or "q." Therefore, statement D is incorrect.
Considering the explanations provided above, the correct answer to the question is none of the options (A, B, C, D).