Graphing Quadratics in Polynomial Form (VCE SSCE Mathematical Methods): Flashcards

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Graphing Quadratics in Polynomial Form
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General form of a quadratic function

y=ax2+bx+cy = ax^2 + bx + c where a0a \neq 0

Y-intercept of y=ax2+bx+cy = ax^2 + bx + c

cc (the constant term)

How to find y-intercept of a quadratic

Substitute x=0x = 0 into the equation

How to find x-intercepts of a quadratic

Set y=0y = 0 and solve for xx

Null factor theorem

If ab=0ab = 0, then a=0a = 0 or b=0b = 0

Axis of symmetry formula (x-intercepts x1x_1, x2x_2)

x=x1+x22x = \frac{x_1 + x_2}{2}

Axis of symmetry is the ... of x-intercepts

Perpendicular bisector

How to find y-coord of turning point

Substitute axis of symmetry x-value into equation

Four steps to sketch quadratic (in order)

Y-intercept, X-intercepts, Axis of symmetry, Turning point

Where is the turning point's x-coordinate?

On the axis of symmetry

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