/Tag: Parabola
26 10, 2016

Discriminant

By |2016-10-26T18:35:14+10:00October 26th, 2016|Tags: , , , |Comments Off on Discriminant

Discriminant $$\Delta=b^2-4ac$$ Δ < 0 - no solutions Δ = 0 - one solution Δ > 0 - two solutions where y = ax2 + bx + c worked examples How many solutions does the equation: y = x2 + 4x + 8 = 0 have? Δ = 42 - 4 × 1 × [...]

16 10, 2016

Parabola Worded Problems

By |2016-10-21T13:16:58+10:00October 16th, 2016|Tags: , , , |Comments Off on Parabola Worded Problems

Parabola Worded Problems worked examples A 20cm piece of wire is bent to form a rectangle. Let x cm be the breadth of the rectangle. a. Use the perimeter to to write an expression for the length of the rectangle in terms of x. b. Write an equation [...]

16 10, 2016

Vertex Of Parabola

By |2016-10-26T18:25:46+10:00October 16th, 2016|Tags: , , , |Comments Off on Vertex Of Parabola

Vertex Of Parabola $$x=-\frac{b}{2a}$$ substitute x to find y if a > 0 concave up ∴ minimum if a < 0 concave down ∴ maximum where y = ax2 + bx + c worked examples Find the vertex of the parabola: y = x2 + 4x + 8. $$x=-\frac{4}{2\times1}$$ using $$x=-\frac{b}{2a}$$ where a = [...]

12 10, 2016

Parabola Axis Of Symmetry

By |2016-10-26T15:16:42+10:00October 12th, 2016|Tags: , , , |Comments Off on Parabola Axis Of Symmetry

Parabola Axis Of Symmetry $$x=-\frac{b}{2a}$$ where y = ax2 + bx + c worked examples Find the axis of symmetry of the parabola: y = x2 + 4x + 8. $$x=-\frac{4}{2\times1}$$ using $$x=-\frac{b}{2a}$$ where a = 1, b = 4 and c = 8 substitute $$x=-\frac42$$ x = -2 simplify [...]

16 06, 2016

Parabola

By |2016-10-21T13:17:02+10:00June 16th, 2016|Tags: , , , |Comments Off on Parabola

Parabola   $$y=x^2$$ Vertex (0, 0) Axis Of Symmetry x = 0 Concave Up $$y=-x^2$$ Vertex (0, 0) Axis Of Symmetry x = 0 Concave Down worked examples On the same axis, draw the graphs of y = x2, y [...]

16 06, 2016

Functions

By |2016-11-30T09:39:15+10:00June 16th, 2016|Tags: , , , , , , |0 Comments

Functions Go to the Functions Forum to see more questions or ask your own Topics Covered in Functions Lines Cubic Hyperbola Exponential Circles Translations Parabola Axis Of Symmetry Vertex Of Parabola Discriminant Parabola Worded Problems Formulas Used in [...]

19 08, 2015

Chord of Contact

By |2017-08-26T08:24:02+10:00August 19th, 2015|Tags: , , , |0 Comments

Chord of Contact $$x.x_0=2a(y + y_0)$$ Find the equation of the chord of contact of tangents from an external point T. Let P(2ap, ap2) and Q(2aq, aq2) be the coordinates of the endpoints of the chord PQ on parabola x2 = 4ay. mPQ = $$\frac{ap^2-aq^2}{2ap-2aq}$$ = $$\frac{a(p-q)(p+q)}{2a(p-q)}$$ = $$\frac{(p+q)}{2}$$ Equation PQ: [...]

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