Karteikarten
Quadratics
Karten in diesem Stapel (23)
- 1Solving quadratic equations by factorisation What do when more complex? when x^2 doesnt =1(x+a)(x+b)
more complex: number before x^2 * c then use factors. Then before first bracket + before second bracket times in bracket then find x - 2X^0 = ?1
- 31^x = ?1
- 4-1^x = ?1
- 5if somethign to hte power = 1 what do?x^0 = 1 so put the power equal to 0
- 6what equation for completing square?(x+a)^2 +b
a(x+b)^2 + c
a-b(x+c)^2 - 7How to solve a(x+b)^2 + cdivide x by number infront of x^2 then do nomral completing spare
- 8Quadratic equationx = -b +/- sqrt b^2 - 4ac / 2a
- 9How do you solve simultatniosu equations?make both = y or x
substitution - 10if more complex what do?make x^2 = y then after do x^2 instead of x so square root remember x = +/- anwser
- 11What is quadratic function general form? What forms on graph?form = ax^2 +bx +c
all have lines of symmetry going through vertex
forms a parabola - 12Starionary/turning pointPoint where gradient = 0
- 13How does orientaiton of parabola depend on?depend on value of a, the coefficient of x^2
if a > 0 the curve has a minimum point that occurs at the lowest point of the curve
if a < 0 the curve has a maxium point (vertex) that occurs at the highest point. Use ocmpleting square or x=0, y = 0 - 14****** What to do if f(x) ax^2 + bx + c is written in form f(x) = a(x-h)^2 + kline of symetry = x=h= -b/2a
if a>0, minimum point at h,k.
if a < 0, maximum point at h,k - 15Solving quadratic inequalitieschekck values y
- 16if f(x) is a function what call the soltion to the equation f(x)=0roots of f(x)
- 17Discriminantpart of the quadratic formula under the square root
- 18what is discriminatnt of ax^2 + bx + c=0discriminant = b^2 - 4ac
in quadratic equation - 19What are the nature of roots of ax^2 + bx +c = 0 and the shape of the curve for b^2-4ac > 02 distinct real roots
2 points line goes over 2 points positive or negative - 20What are the nature of roots of ax^2 + bx +c = 0 and the shape of the curve for b^2-4ac = 02 equal roots (or 1 repeated real root)
just one point line crosses on curve negative or possitive - 21What are the nature of roots of ax^2 + bx +c = 0 and the shape of the curve for b^2-4ac < 0no real roots
no points line don't touch graph - 22What are the 3 possible situations of a straight line and a parabola?2 points of intersection: line cuts cure at 2 distinct points: b^2-4ac>0
1 point of interception: line is a tangent to the curve: b^2-4ac = 0
0 point of interception: line doesn't intersect curve b^2-4ac < 0 - 23What does min point =? on completing square?-p,q
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- A Level A Level Maths (Pure Maths 1) Karteikarten am Quadratics, erstellt von HRYN red am 13/04/2022.
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- HRYN red
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