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2.05 Using quadratic functions

Interactive practice questions

A parabola of the form $y=ax^2$y=ax2 goes through the point $\left(2,-4\right)$(2,4).

a

What is the value of $a$a?

b

What are the coordinates of the vertex?

Vertex $=$=$\left(\editable{},\editable{}\right)$(,)

c

Plot the graph of the parabola.

Loading Graph...
Easy
2min

Consider the graph.

Easy
2min

A parabola has its turning point at $x=-3$x=3 and one of the $x$x-intercepts is $x=1$x=1.

Medium
6min

Write down the equation of the parabola that has the same shape as $f\left(x\right)=6x^2$f(x)=6x2, and vertex at $\left(-2,3\right)$(2,3):

Easy
1min
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Outcomes

1.2.2.1

examine examples of quadratically related variables

1.2.2.4

identify contexts suitable for modelling with quadratic functions and use models to solve problems with and without technology; verify and evaluate the usefulness of the model using qualitative statements and quantitative analysis

1.2.2.5

understand the role of the discriminant to determine the number of solutions to a quadratic equation

1.2.2.6

determine turning points and zeros of quadratic functions with and without technology

1.2.4.7

solve equations involving combinations of the functions above, using technology where appropriate

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