Identifying Characteristics of Quadratic Functions
Identify axis of symmetry, vertex, and parabola direction for Grade 9 quadratic functions using the formula x = -b divided by 2a.
Key Concepts
New Concept The axis of symmetry for the graph of a quadratic equation $y = ax^2 + bx + c$ is $x = \frac{b}{2a}$. What’s next Next, you’ll apply this formula and other tools to analyze the key features of parabolas, like their vertex and zeros.
Common Questions
How do you find the axis of symmetry of a quadratic function?
Use x = -b/(2a) from standard form ax^2+bx+c. For y = 2x^2-8x+3, the axis is x = -(-8)/(2 times 2) = 8/4 = 2.
What does the axis of symmetry tell you about a parabola?
It gives the x-coordinate of the vertex and divides the parabola into two mirror-image halves. Points equidistant from this line have equal y-values.
How do coefficients a, b, and c affect the parabola's graph?
The sign of a determines direction (up if a>0, down if a<0). The vertex x-coordinate depends on -b/(2a). The c-value is the y-intercept.