The two zeros of an unknown quadratic function f(x) are (−6, 0) and (8, 0). Which of the following is the axis of symmetry of f(x)?(1 point)
x=7
x = 1
x=−7
x =−1
so x=1
The axis of symmetry will cut the x-axis half-way between the two zeros,
so .....
To find the axis of symmetry of a quadratic function, you can use the formula x = -b/ (2a), where ax^2 + bx + c = 0 is the standard form of the quadratic equation.
In this case, since the zeros of the function are (-6, 0) and (8, 0), we can see that the quadratic function can be expressed as (x + 6)(x - 8) = 0. Expanding this equation, we get x^2 - 2x - 48 = 0.
Comparing this equation to the standard form ax^2 + bx + c = 0, we have a = 1, b = -2, and c = -48.
Using the formula for the axis of symmetry, we can substitute the values of a and b into the equation:
x = -(-2) / (2 * 1)
x = 2/2
x = 1
Therefore, the axis of symmetry of the function f(x) is x = 1.
Hence, the correct answer is x = 1.
To find the axis of symmetry of a quadratic function, we need to use the formula x = -b / (2a), where the quadratic function is in the form f(x) = ax^2 + bx + c.
In this case, we are given the two zeros of the quadratic function f(x), which are (-6, 0) and (8, 0). The zeros correspond to the x-intercepts, which means that the quadratic function crosses the x-axis at these points.
Since the zeros are given as points, we can write two equations using these points. The equations are:
1) -6 = a(-6)^2 + b(-6) + c
2) 8 = a(8)^2 + b(8) + c
We can simplify these equations by substituting the value of y (which is 0) for each equation:
1) 0 = a(-6)^2 + b(-6) + c
2) 0 = a(8)^2 + b(8) + c
Substituting the x-values, we get:
1) 0 = 36a - 6b + c
2) 0 = 64a + 8b + c
Next, solve this system of equations to find the values of a, b, and c.
From equation 1, we get: c = 6b - 36a
Substitute this value of c in equation 2:
0 = 64a + 8b + (6b - 36a)
Rearranging the terms, we get:
0 = 28a + 14b
Now, we have two equations:
1) c = 6b - 36a
2) 0 = 28a + 14b
We can eliminate one variable by solving these two equations simultaneously. Dividing equation 2 by 14, we get:
0 = 2a + b
Substitute this value of b in equation 1:
c = 6(0 - 2a) - 36a
c = -12a - 36a
c = -48a
So the equation of the quadratic function is: f(x) = ax^2 + bx + c = ax^2 + (0 - 2a)x + (-48a)
Now, to find the axis of symmetry, we use the formula x = -b / (2a). Since the coefficient of x is -2a in the equation, the axis of symmetry will be x = -(-2a) / (2a) = 2a / (2a) = 1.
Therefore, the correct answer is x = 1.