Need help with parabolas (1 Viewer)

iamastar · Jun 28, 2016

Determine the equation of the quadratic expression for each table of values. How do you find this out? Is there a formula?

Help is appreciated, I'm in Year 10.

InteGrand · Jun 28, 2016

iamastar said:
Determine the equation of the quadratic expression for each table of values. How do you solve this? Is there a formula?

Help is appreciated

$\noindent One way is to let the quadratic be $y=ax^2 + bx + c$, sub. in three given $(x,y)$ pairs, and solve the resulting three simultaneous equations in the three unknowns $a,b,c$. If we know it's a quadratic like this, we only need three points to do it.$

$\noindent However, in each of these datasets, we can see where the quadratic's axis of symmetry is. This lets us write $y= A\left(x-h\right)^2 + k$, where $x=h$ is the vertical line that is the axis of symmetry, and $k$ is the corresponding $y$ value here (i.e. $(h,k)$ is the vertex). So since we can deduce the vertex, we need only deduce the value of $A$, which we can do by subbing in one other point.$

InteGrand · Jun 28, 2016

iamastar · Jun 28, 2016

Hey, how do you know, or deduce - from the table of values - what the axis of symmetry is?

InteGrand · Jun 28, 2016

iamastar said:
Hey, how do you know, or deduce - from the table of values - what the axis of symmetry is?

It's the place where on either side when you increment x by some amount, the y-values are the same.

For example for the first one the y-values are seen to be symmetrical about the x = 0 column, which implies the axis of symmetry is x = 0.

(In fact, just having one pair of symmetric values at equally spaced distances from a certain x-value is enough to imply that this x-value is the axis of symmetry.)

davidgoes4wce · Jun 28, 2016

Part (a)

davidgoes4wce · Jun 29, 2016

Part (b)

davidgoes4wce · Jun 29, 2016

Part (c)

davidgoes4wce · Jun 29, 2016

Part (d)

Need help with parabolas (1 Viewer)

iamastar

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