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NSWMaths Standard 2Quick questions

Year 12: Algebra

Quick questions on Quadratic models for HSC Maths Standard 2

10short 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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$y=ax2+bx+c,a≠0.y = a x^2 + b x + c, \quad a \neq 0.$
What is finding the vertex?
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The vertex (highest or lowest point) occurs at
What is zeros (where y=0y = 0)?
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The discriminant Δ=b2−4ac\Delta = b^2 - 4 a c tells you how many real zeros there are: two if Δ>0\Delta > 0, one if Δ=0\Delta = 0, none if Δ<0\Delta < 0.
What is yy-intercept?
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Set x=0x = 0. The yy-intercept is just cc.
What is practical contexts?
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:::worked Worked example ### Projectile
What is maximum profit (Australian example)?
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A market stall sells avocados. At \3eachtheysell each they sell 80perday.Forevery per day. For every \0.100.10 increase, sales drop by 55 per day. Cost is \1.50$ per avocado.
What is discarding the wrong root?
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In a projectile problem, only the positive tt value matters. In an area or revenue problem, only the value that gives a positive quantity matters.
What is forgetting that downward parabola has a maximum?
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a<0a < 0 opens downward, so the vertex is the highest point. Markers expect you to state this.
What is using the wrong formula for the vertex?
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It is x=−b2ax = -\frac{b}{2a}, not b2a\frac{b}{2a}. Sign error costs marks.
What is not substituting back for the maximum value?
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Finding the xx-coordinate is half the job. The question usually asks for the maximum or minimum yy. :::

All Maths Standard 2Q&A pages