📚 Topic Summary
Parabolas are U-shaped curves that represent quadratic equations. The general form of a quadratic equation is $y = ax^2 + bx + c$. The vertex is the turning point of the parabola, and the axis of symmetry is the vertical line that passes through the vertex, dividing the parabola into two symmetrical halves. Graphing parabolas involves finding the vertex, axis of symmetry, y-intercept, and possibly x-intercepts (roots or zeros) to accurately sketch the curve.
Understanding how the 'a' value affects the shape and direction (opening upwards or downwards) of the parabola is crucial. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards. The larger the absolute value of 'a', the narrower the parabola.
🧠 Part A: Vocabulary
Match the following terms with their correct definitions:
- Vertex
- Axis of Symmetry
- Parabola
- Quadratic Equation
- Y-intercept
Definitions:
- A U-shaped curve.
- The point where the parabola intersects the y-axis.
- The turning point of a parabola.
- An equation of the form $y = ax^2 + bx + c$.
- The vertical line through the vertex that divides the parabola into two symmetrical halves.
📝 Part B: Fill in the Blanks
Complete the following paragraph using the words provided:
(Opens, Vertex, Negative, Positive, Axis of Symmetry)
A parabola ______ upwards if the 'a' value in the quadratic equation is ______. The turning point of the parabola is called the ______. The ______ is a line that divides the parabola into two equal halves. If 'a' is ______, the parabola opens downwards.
💡 Part C: Critical Thinking
Explain how changing the 'a' value in the quadratic equation $y = ax^2 + bx + c$ affects the shape and direction of the parabola.