Quadratic Graphs (Edexcel A-Level Mathematics): Quizzes

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Quadratic Graphs
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What is the graph of a quadratic function called?

A parabola

If a>0a > 0 in y=ax2+bx+cy = ax^2 + bx + c, which way does the parabola open?

Upwards (U shape)

If a<0a < 0 in y=ax2+bx+cy = ax^2 + bx + c, which way does the parabola open?

Downwards (inverted U)

What does the vertex represent when a>0a > 0?

The minimum point

What is the formula for the xx-coordinate of the vertex?

x=−b2ax = -\frac{b}{2a}

What is the equation of the axis of symmetry?

x=−b2ax = -\frac{b}{2a}

What is the yy-intercept of y=ax2+bx+cy = ax^2 + bx + c?

(0,c)(0, c)

What are the xx-intercepts also called?

Roots or zeros

If b2−4ac>0b^2 - 4ac > 0, how many real roots are there?

Two distinct real roots

If b2−4ac=0b^2 - 4ac = 0, how many real roots are there?

One real root (repeated)

If b2−4ac<0b^2 - 4ac < 0, what happens to the parabola?

It does not cross the xx-axis

What is the quadratic formula for solving ax2+bx+c=0ax^2 + bx + c = 0?

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

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