Solving Simultaneous Linear and Quadratic Equations (VCE SSCE Mathematical Methods): Quizzes

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Solving Simultaneous Linear and Quadratic Equations
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What do we find when solving simultaneous linear and quadratic equations?

Where a straight line and parabola intersect

How many points of intersection can a straight line have with a parabola?

0, 1, or 2

What is a tangent to a parabola?

A line that touches the curve at one point

What is the first step in the substitution method?

Write both equations with yy as subject

After writing both equations with yy as subject, what do we do next?

Set the two expressions equal and solve

For y=2x+4y = -2x + 4 and y=x28x+12y = x^2 - 8x + 12, what are the intersection points?

(2,0)(2, 0) and (4,4)(4, -4)

After finding xx-values, how do we find corresponding yy-values?

Substitute into either original equation

What does a perfect square like (x1)2=0(x - 1)^2 = 0 indicate?

The line is a tangent (one solution)

For y=1xy = 1 - x and y=x23x+2y = x^2 - 3x + 2, where do they meet?

(1,0)(1, 0) only

What is the rearranged form of x28x+12=2x+4x^2 - 8x + 12 = -2x + 4?

x26x+8=0x^2 - 6x + 8 = 0

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