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2.06 Quadratic functions

Interactive practice questions

Consider the general quadratic equation $y=ax^2+bx+c$y=ax2+bx+c, $a\ne0$a0. Which of the following statements about the parabola described by this equation is true?

The parabola will open to the left if $a<0$a<0, and will open to the right if $a>0$a>0.

A

The parabola will open upwards if $a>0$a>0, and will open downwards if $a<0$a<0.

B

The parabola will open upwards if $a<0$a<0, and will open downwards if $a>0$a>0.

C

The parabola will open to the left if $a>0$a>0, and will open to the right if $a<0$a<0.

D
Easy
< 1min

Does the parabola represented by the equation $y=x^2-8x+9$y=x28x+9 open upward or downward?

Easy
< 1min

The graph of $y=x^2+6$y=x2+6 has no $x$x-intercepts.

True or False?

Easy
< 1min

Consider the given graph and answer the following questions.

Easy
1min
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Outcomes

1.1.7

examine examples of quadratically related variables

1.1.8

recognise features of the graphs of y=x^2, y=a(x-b)^2 and y=a(x−b)(x−c) including their parabolic nature, turning points, axes of symmetry and intercepts

1.1.12

recognise features of the graph of the general quadratic y=ax^2+bx+c

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