Quadratic (Leaving Cert Mathematics): Quizzes

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Quadratic
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What is the graph of a quadratic function called?

A parabola

What is the general form of a quadratic function?

y=ax2+bx+cy = ax^2 + bx + c

If a>0a > 0 in y=ax2+bx+cy = ax^2 + bx + c, what shape does the parabola have?

Opens upwards (U shape)

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

Opens downwards

When a>0a > 0, what does the vertex represent?

The minimum point

When a<0a < 0, what does the vertex represent?

The maximum point

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

x=−b2ax = -\frac{b}{2a}

What is the equation of the axis of symmetry?

x=−b2ax = -\frac{b}{2a}

In y=ax2+bx+cy = ax^2 + bx + c, what is the y-intercept?

(0,c)(0, c)

If b2−4ac>0b^2 - 4ac > 0, how many real roots does the quadratic have?

Two distinct real roots

If b2−4ac=0b^2 - 4ac = 0, how many real roots does the quadratic have?

One real root (repeated)

If b2−4ac<0b^2 - 4ac < 0, what can be said about the roots?

There are no real roots

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