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expanded form y = ax 2 +bx+c

QUADRATIC FUNCTIONS. Three different ways to write the equation of the same quadratic function. expanded form y = ax 2 +bx+c. factorised form y = a(x-m)(x-n ). turning point form y = a(x-h) 2 + k. QUADRATIC FUNCTIONS. How to change from one form to another.

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expanded form y = ax 2 +bx+c

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  1. QUADRATIC FUNCTIONS Three different ways to write the equation of the same quadratic function expanded formy = ax2+bx+c factorised form y = a(x-m)(x-n) turning point form y = a(x-h)2 + k

  2. QUADRATIC FUNCTIONS How to change from one form to another expanded formy = ax2+bx+c complete the square factorise expand expand Write as difference of two squares and factorise factorised form y = a(x-m)(x-n) turning point form y = a(x-h)2 + k

  3. QUADRATICFUNCTIONS Links between symbols and graphs c is the y-intercept and a gives the dilation and reflection expanded form y = ax2+bx+c complete the square factorise expand expand product of factors y = a(x-m)(x-n) turning point form y = a(x-h)2 + k m and n are the x-intercepts and a gives the dilation and reflection (h, k) is the turning point and a gives the dilation and reflection

  4. QUADRATICFUNCTIONS Calculating values of coordinates for points on the graph • Turning point: (h, k) • Write in turning point form by completing the square and read off h and k. • or • use and calculate the value of k by substituting the value of h into the equation as the x value. • y - intercept: • Let x = 0 in the equation and then simplify the equation. • Calculate the value of y when x = 2: • Let x = 2 in the equation and then simplify the equation. y = 1 • x - intercepts: • Let y = 0 in the equation and then solve the equation. • (See next slide for how to solve quadratic equations) • Calculate the value of x when y = 1: • Let y = 1 in the equation and then solve the equation. • (See next slide for how to solve quadratic equations) x = 2

  5. SOLVING QUADRATIC EQUATIONS Use quadratic formula or change to another form expanded formax2+bx+c = 0 complete the square factorise expand expand factorised form a(x-m)(x-n) = 0 turning point form a(x-h)2 + k = 0 Use the null factor law: Either x-m = 0 and/or x-n = 0 Use ‘undoing’ or “doing the same to both sides”: a(x-h)2= - k and so on

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