What is a Quadratic function? A Quadratic function is a function that has the form y=ax²+bx+c. When it is graphed it is a parabola. The parabola can be.

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Presentation transcript:

What is a Quadratic function? A Quadratic function is a function that has the form y=ax²+bx+c. When it is graphed it is a parabola. The parabola can be upright or upsidedown depending on the sing of “a”. It can also be wider or skiner depending on the absolute value of “a”

Quadratic functionsLinear function Standard form: Y=ax²+bx+c Vertex form: y=a(x-h) ²+k When it is graph it is a parabola One variable solved for x When it is graph it is a line Slope= rise/run -> y₁-y₂/x₁-x₂ Slope intercept form: y=mx+b Point slope form: y-y₁ = m (x-x₁)

Quadratics: Linear: 1. Y= 3x²+2x-7 2.Y= 7x²-9x-8 3.Y=-2x²+10x-5 1. Y= 2x-7 2.Y= 9x-8 3.Y=-10x-5

To graph quadric functions you use : y=a(x-b) ²+c  C: Moves vertex up or down C units positive goes up Negative goes down  B: Moves vertex left or right B units Positive – left Negative - right  A: Less than 0 – Goes down (like a rainbow) More than 0- Goes up (like a horse shoe). Greater than 1 – skinier Less than 1 - wider Less than 0 More than 0

When the parabola opens up, it has a minimum value at the vertex and when it opens down it has a maximum value at the vertex.

STEPS: 1.GRAPH THE FUNCTION IDENTIFY A, B AND C CALCULATE BY USING –B/(2 A) BY PLUGGING IN THE NUMBERS. USE T-TABLE TO GRAPH 2.FIND X-INTERCEPT(S) ON THE GRAPH 3.YOUR SOLUTIONS ARE THE X- INTERCEPTS.

1.Leave X² alone 2.Find the square root of the numbers 3.If the one of the numbers or the number has no exact square root, then factor the number and find the square root of one or both of thoes numbers. 4.Then write pluss minus infront the number.

STEPS: 1.WRITE THE EQUATION IN STANDARD FORM 2.FIND GCF 3.CANCEL GRATEST COMMON FACTOR BY DIVIDING THAT NUMBER ON BOTH SIDES 4.FACTOR THE TRINOMIAL 5.EQUAL EACH FACTOR TO 0 6.SOLVE EACH LINEAR EQUATION

Steps: 1.The coeficient of X² must be =1 2.Isolate C 3.Complete the square 4.Add (b/2)² to both sides 5.Write as a binomial squared. 6.Solve by using square root both sides 7.Dont forget the +- (pluss minus) 8.Isolate the variable

Steps: 1.Write in standard form your equation. 2.Find a, b, c 3.Plug them in the formula 4.solve The Quadratic Formula:

To solve a quadratic eqation we can first calculate the discriminant to determine number of solutions. If the discriminant is positive, the equation has two solutions. If it is 0 it has one solution. If it is negative, then the equation has no real solution.