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Expanding and Binomials

Expanding Double Brackets

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Simple Quadratic Equations

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Converting Quadratics: Standard Form and Vertex Form

How to Write Quadratic Equations in Vertex Form and Standard Form

Solving Simple Quadratic Equations

Solving Quadratic Equations by Factorising

Solving Quadratic Equations: Quadratic Formula

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Simple Quadratic Equations

Algebra and Graphs Simple Quadratic Equations

🎬 Video Tutorial

(0:01) Definition of Quadratic Equations: Quadratic equations contain an $x^2$ term; the standard form is $y = ax^2 + bx + c$ ($a \neq 0$).
(1:24) Role of Coefficient $a$: The sign of $a$ affects the parabola’s direction. If $a > 0$, the parabola opens upwards; if $a < 0$, it opens downwards.
(1:48) Effect of $|a|$ on Width: The larger the absolute value of $a$, the narrower the parabola. The smaller the absolute value of $a$, the wider the parabola.
(2:25) Vertex and Symmetry: For $y = ax^2$, the vertex is at $(0,0)$, and the parabola is symmetric about the $y$-axis because $x^2$ and $(-x)^2$ yield the same $y$-value.

📂 Revision Cards

Quadratic equation formula y = ax² with a not equal to zero, highlighting coefficient 'a'.

Graph of the quadratic equation y = x² with a table of x and y values and a standard parabola on a coordinate plane where a = 1.

Graph illustrating how the sign of "a" affects direction and its absolute value affects the width of the parabola.

🍪 Quiz Time - Practice Now!

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Simple Quadratic Equations

1 / 6

Q: What happens when $a$ is positive in a quadratic equation?

The parabola opens downward

The parabola becomes wider

The parabola has no symmetry

The parabola opens upward

Feedback: Not quite! When $a$ is positive, the parabola opens upward.

Feedback: Well done! When $a$ is positive, the parabola opens upward.

2 / 6

Q: What can you tell about the parabola if $a$ is negative in a quadratic equation?

The parabola has no symmetry

The parabola opens downward

The parabola opens upward

The parabola becomes wider

Feedback: Not quite! When $a$ is negative, the parabola opens downward. The width of the parabola depends on the absolute value of $a$. Without knowing the exact value of $a$, we can't determine if the parabola is wide or narrow.

Feedback: Well done! When $a$ is negative, the parabola opens downward. The width of the parabola depends on the absolute value of $a$. Without knowing the exact value of $a$, we can't determine if the parabola is wide or narrow.

3 / 6

Q: If $a = 4$, how does the parabola change compared to when $a = 1$?

The parabola opens downward and is narrower

The parabola opens upward and is wider

The parabola opens downward and is wider

The parabola opens upward and is narrower

Feedback: Not quite! When $a = 4$, the parabola opens upward because $a$ is positive. Since the absolute value of $a$ is greater than 1, the parabola becomes narrower compared to when $a = 1$.

Feedback: Well done! When $a = 4$, the parabola opens upward because $a$ is positive. Since the absolute value of $a$ is greater than 1, the parabola becomes narrower compared to when $a = 1$.

4 / 6

Q: If $a = 0.5$, how does the parabola change compared to when $a = 1$?

The parabola opens downward and is wider

The parabola opens upward and is wider

The parabola opens downward and is narrower

The parabola opens upward and is narrower

Feedback: Not quite! When $a = 0.5$, the parabola opens upward because $a$ is positive. Since the absolute value of $a$ is less than 1, the parabola is wider compared to when $a = 1$. A smaller value of $a$ makes the curve flatter.

Feedback: Well done! When $a = 0.5$, the parabola opens upward because $a$ is positive. Since the absolute value of $a$ is less than 1, the parabola is wider compared to when $a = 1$. A smaller value of $a$ makes the curve flatter.

5 / 6

Q: If $a = -2$, how does the parabola change compared to when $a = 1$?

The parabola opens downward and is wider

The parabola opens downward and is narrower

The parabola opens upward and is narrower

The parabola opens upward and is wider

Feedback: Not quite! When $a = -2$, the parabola opens downward because $a$ is negative. Since the absolute value of $a$ is greater than 1, the parabola is narrower compared to when $a = 1$.

Feedback: Well done! When $a = -2$, the parabola opens downward because $a$ is negative. Since the absolute value of $a$ is greater than 1, the parabola is narrower compared to when $a = 1$.

6 / 6

Q: If $a = -0.5$, how does the parabola change compared to when $a = 1$?

The parabola opens upward and is narrower

The parabola opens downward and is wider

The parabola opens upward and is wider

The parabola opens downward and is narrower

Feedback: Not quite! When $a = -0.5$, the parabola opens downward because $a$ is negative. Since the absolute value of $a$ is less than 1, the parabola is wider compared to when $a = 1$. A smaller absolute value of $a$ makes the curve flatter.

Feedback: Well done! When $a = -0.5$, the parabola opens downward because $a$ is negative. Since the absolute value of $a$ is less than 1, the parabola is wider compared to when $a = 1$. A smaller absolute value of $a$ makes the curve flatter.

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