a and b are coefficients of x2 and x respectively.
c is a constant term.
Example 1:
Find the axis of symmetry of the graph of y =
Solution:
Given,
y = x2 – 6x + 5
For a quadratic function in standard form, y = a
Substituting the values of a and b,
x = -(-6)/2(1)
= 6/2
= 3
Therefore, the axis of symmetry is x = 3.
Example 2:
Find the axis of symmetry of the graph of y = 2x2 + 8x – 3, using the formula.
Solution:
Given,
y = 2x2 + 8x – 3
Comparing the given equation with the standard form y = ax2 + bx + c,
a = 2, b = 8, c = -3
And the axis of symmetry is a vertical line; x = -b/2a
Substituting the values of a and b,
x = -8/2(2)
= -8/4
= -2
Therefore, the axis of symmetry is x = -2.
Example 3:
If the axis of symmetry of the equation y = px2 – 12x – 5 is 2, then find the value of p.
Solution:
Given,
y = px2 – 12x – 5
Axis of symmetry is x = 2
For a quadratic function in standard form, y=a
Here, a = p, b = -12, c = -5
According to the given,
-b/2a = 2
-(-12)/2p = 2
12 = 4p
12/4 = p
Therefore, p = 3
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