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VICMath MethodsQuick questions

Unit 1: Functions, relations and graphs

Quick questions on Quadratic functions and parabolas (VCE Maths Methods Unit 1)

7short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is standard form?
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y=ax2+bx+cy = ax^2 + bx + c. Coefficient aa controls opening (up if a>0a > 0, down if a<0a < 0) and steepness. cc is the yy-intercept.
What is factored form?
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y=a(x−p)(x−q)y = a(x - p)(x - q). Roots are at x=px = p and x=qx = q. Useful when roots are known.
What is turning-point form?
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y=a(x−h)2+ky = a(x - h)^2 + k. Vertex at (h,k)(h, k). Axis of symmetry x=hx = h.
What is vertex form's hh has the opposite sign to the bracket?
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(x−3)2(x - 3)^2 gives h=+3h = +3, not −3-3.
What is q1?
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For y=x2−6x+5y = x^2 - 6x + 5, find the vertex and the xx-intercepts. [3 marks]
What is q2?
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Find the values of kk for which x2+kx+9=0x^2 + kx + 9 = 0 has exactly one solution. [3 marks]
What is q3?
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A fountain's water arc is y=−0.5(x−4)2+8y = -0.5(x - 4)^2 + 8 (metres). (a) State the maximum height and where it occurs. (b) Find where the water lands (y=0y = 0).

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