The function f(x) = ax^2 + bx + c is a quadratic function. The graph of a quadratic function is a parabola. If the graph passes through the points (7,0) and (-3,0), these are the x-intercepts of the parabola, meaning the function equals zero at these points.

So, we can set up the following equations based on the function:

a(7)^2 + b(7) + c = 0
a(-3)^2 + b(-3) + c = 0

This simplifies to:

49a + 7b + c = 0
9a - 3b + c = 0

We know that the coefficient a is an integer greater than 1, but we don't know the values of b and c. However, we are asked to find the possible value of a + b.

Since we have two equations, we can subtract the second equation from the first to eliminate c:

49a + 7b + c - (9a - 3b + c) = 0 - 0

This simplifies to:

40a + 10b = 0

Divide through by 10:

4a + b = 0

So, a + b = -4a. Since a is an integer greater than 1, a + b must be a negative number. The only negative options given are A) -6 and B) -3.

Without knowing the exact value of a, we can't determine the exact value of a + b. However, if a is 2 (the smallest integer greater than 1), then a + b = -4(2) = -8, which is less than both -6 and -3.

Therefore, none of the given options could be the value of a + b.

Question

The function f(x) = ax^2 + bx + c is a quadratic function. The graph of a quadratic function is a parabola. If the graph passes through the points (7,0) and (-3,0), these are the x-intercepts of the parabola, meaning the function equals zero at these points.

So, we can set up the following equations based on the function:

a(7)^2 + b(7) + c = 0
a(-3)^2 + b(-3) + c = 0

This simplifies to:

49a + 7b + c = 0
9a - 3b + c = 0

We know that the coefficient a is an integer greater than 1, but we don't know the values of b and c. However, we are asked to find the possible value of a + b.

Since we have two equations, we can subtract the second equation from the first to eliminate c:

49a + 7b + c - (9a - 3b + c) = 0 - 0

This simplifies to:

40a + 10b = 0

Divide through by 10:

4a + b = 0

So, a + b = -4a. Since a is an integer greater than 1, a + b must be a negative number. The only negative options given are A) -6 and B) -3.

Without knowing the exact value of a, we can't determine the exact value of a + b. However, if a is 2 (the smallest integer greater than 1), then a + b = -4(2) = -8, which is less than both -6 and -3.

Therefore, none of the given options could be the value of a + b.

Knowee AI · Accepted Answer

The function f(x) = ax^2 + bx + c is a quadratic function. The graph of a quadratic function is a parabola. If the graph passes through the points (7,0) and (-3,0), these are the x-intercepts of the parabola, meaning the function equals zero at these points.

So, we can set up the following equations based on the function:

a(7)^2 + b(7) + c = 0
a(-3)^2 + b(-3) + c = 0

This simplifies to:

49a + 7b + c = 0
9a - 3b + c = 0

We know that the coefficient a is an integer greater than 1, but we don't know the values of b and c. However, we are asked to find the possible value of a + b.

Since we have two equations, we can subtract the second equation from the first to eliminate c:

49a + 7b + c - (9a - 3b + c) = 0 - 0

This simplifies to:

40a + 10b = 0

Divide through by 10:

4a + b = 0

So, a + b = -4a. Since a is an integer greater than 1, a + b must be a negative number. The only negative options given are A) -6 and B) -3.

Without knowing the exact value of a, we can't determine the exact value of a + b. However, if a is 2 (the smallest integer greater than 1), then a + b = -4(2) = -8, which is less than both -6 and -3.

Therefore, none of the given options could be the value of a + b.

Question

Solution

Similar Questions

Upgrade your grade with Knowee