📄 GCSE Maths (Foundation): Quadratics and Graphing Worksheet
📌 1. True / False
1. The graph of a quadratic equation is always a straight line.
2. A quadratic equation always has a term with \(x^2\).
3. The 'roots' of a quadratic equation are the points where its graph crosses the y-axis.
4. The turning point of a parabola can be either a maximum or a minimum point.
5. The equation \(y = 2x + 5\) is a quadratic equation.
✏️ 2. Fill in the Blanks
🔗 3. Matching
✍️ 4. Short Answer Questions
1. Explain how you can tell if an equation is quadratic by looking at its terms.
2. What does it mean for a quadratic graph to 'open upwards'?
🎯 5. Multiple Choice
1. Which of the following equations represents a quadratic function?
2. What is the name given to the graph of a quadratic function?
3. For the quadratic graph \(y = x^2 - 4x + 3\), what are the coordinates of the y-intercept?
📝 6. Open-Ended Questions
1. a) Complete the table of values for \(y = x^2 - 2x - 3\) for x from -2 to 4.
b) Plot the graph of \(y = x^2 - 2x - 3\) on a coordinate grid.
c) Use your graph to find the roots of the equation \(x^2 - 2x - 3 = 0\).
2. The graph of \(y = x^2 - 2x - 8\) is shown below. (Assume a graph is provided to the student).
a) Identify the coordinates of the turning point of the graph.
b) Use the graph to estimate the values of x when \(y = -5\).
3. A quadratic equation is given by \(x^2 + 5x + 6 = 0\).
a) Factorise the quadratic expression \(x^2 + 5x + 6\).
b) Use your factorisation to solve the equation \(x^2 + 5x + 6 = 0\).
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Name Surname: .................................. Date: .... / .... / 202...
Quadratics and Graphing Worksheet
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SCORE
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A. True (T) / False (F)
| ( .... ) | The graph of a quadratic equation is always a straight line. |
| ( .... ) | A quadratic equation always has a term with \(x^2\). |
| ( .... ) | The 'roots' of a quadratic equation are the points where its graph crosses the y-axis. |
| ( .... ) | The turning point of a parabola can be either a maximum or a minimum point. |
| ( .... ) | The equation \(y = 2x + 5\) is a quadratic equation. |
B. Fill in the Blanks
| 1) | The graph of a quadratic equation is called a ..................... |
| 2) | The highest or lowest point on a quadratic graph is known as the .................... point. |
| 3) | A quadratic equation is typically written in the form \(ax^2 + bx + c = 0\), where \(a \neq 0\). |
| 4) | The solutions to a quadratic equation are also referred to as its ..................... |
| 5) | The vertical line that divides a parabola into two symmetrical halves is called the axis of ..................... |
C. Matching Concepts
| ( .... ) | An equation where the highest power of the variable is 2. | - Roots |
| ( .... ) | The U-shaped curve that is the graph of a quadratic function. | - Axis of Symmetry |
| ( .... ) | The x-values where the graph of a quadratic equation crosses the x-axis. | - Quadratic Equation |
| ( .... ) | The point on a parabola where the graph changes direction (minimum or maximum). | - Turning Point |
| ( .... ) | A vertical line that divides the parabola into two mirror images. | - Parabola |
D. Short Answer Questions
| 1) | Explain how you can tell if an equation is quadratic by looking at its terms. |
| 2) | What does it mean for a quadratic graph to 'open upwards'? |
E. Multiple Choice Questions
| 1) |
Which of the following equations represents a quadratic function?
A) \(y = 3x - 1\)
B) \(y = x^2 + 2x - 5\)
C) \(y = 4x^3 + x\)
D) \(y = \frac{1}{x}\)
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| 2) |
What is the name given to the graph of a quadratic function?
A) Hyperbola
B) Parabola
C) Ellipse
D) Circle
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| 3) |
For the quadratic graph \(y = x^2 - 4x + 3\), what are the coordinates of the y-intercept?
A) (0, 3)
B) (3, 0)
C) (0, -4)
D) (1, 0)
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F. Open-Ended Questions
| 1) |
a) Complete the table of values for \(y = x^2 - 2x - 3\) for x from -2 to 4. b) Plot the graph of \(y = x^2 - 2x - 3\) on a coordinate grid. c) Use your graph to find the roots of the equation \(x^2 - 2x - 3 = 0\). |
| 2) |
The graph of \(y = x^2 - 2x - 8\) is shown below. (Assume a graph is provided to the student). a) Identify the coordinates of the turning point of the graph. b) Use the graph to estimate the values of x when \(y = -5\). |
| 3) |
A quadratic equation is given by \(x^2 + 5x + 6 = 0\). a) Factorise the quadratic expression \(x^2 + 5x + 6\). b) Use your factorisation to solve the equation \(x^2 + 5x + 6 = 0\). |
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