Axis of symmetry
Find the axis of symmetry of a parabola in Grade 10 algebra using x = -b/(2a) from standard form, and use it to locate the vertex and graph quadratic functions accurately.
Key Concepts
The axis of symmetry is a vertical line that divides a parabola into two congruent mirror images. The equation for this line is $x = \frac{b}{2a}$.
For the function $f(x) = x^2 x 6$, where $a=1$ and $b= 1$, the axis of symmetry is $x = \frac{( 1)}{2(1)} = \frac{1}{2}$. Given $f(x) = 2x^2 12x + 5$, where $a=2$ and $b= 12$, the axis of symmetry is $x = \frac{( 12)}{2(2)} = \frac{12}{4} = 3$.
Imagine folding a paper parabola perfectly in half; the crease line is its axis of symmetry! It's a vertical line that cuts right through the vertex, making the left side a perfect mirror image of the right. The magic formula $x = \frac{b}{2a}$ instantly gives you this line for any quadratic in standard form.
Common Questions
What is the formula for the axis of symmetry of a parabola?
For f(x) = ax²+bx+c, the axis of symmetry is the vertical line x = -b/(2a). It passes through the vertex and divides the parabola into two mirror-image halves.
Find the axis of symmetry for f(x) = 2x²-8x+3.
x = -(-8)/(2·2) = 8/4 = 2. The axis of symmetry is the line x=2.
How do you use the axis of symmetry to find the vertex?
Find x = -b/(2a), then substitute that x-value into the function to get the y-coordinate. For f(x)=2x²-8x+3 with x=2: f(2)=8-16+3=-5. Vertex is (2,-5).