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CPM Unit 8 Key Quest

Graphing Quadratics

QuestionAnswer
Highest or lowest point of a parabola vertex
Where the line crosses the y axis; y-intercept
Where the graph crosses the x-axis; also zero or root; y=0 x-intercept
Where the function equals zero; also x-intercept or root zero
A solution of an equation; also x value of x-intercept or zero root
The vertical line through the vertex; x= the x-value of the vertex axis or line of symmetry
What form is: y=ax²+bx+c standard form of a quadratic
What form is: f(x)=a(x-h)² + k where (h,k) is the vertex vertex form of a quadratic
What form is: ƒ(x)=a(x-r₁)(x-r₂) where r₁ & r₂ are the roots root form of a quadratic
A parabola faces up when a≥0
A parabola faces down when a≤0
A parabola gets wider as |a| approaches zero
A parabola gets narrower as |a| approaches infinity
How do you graph a parabola from any form? y=a(x-h)²+k Find the vertex Find two points left and two points right of the vertex Graph the vertex Graph the line (or axis) of symmetry Graph each of the other two symmetric pairs Draw the parabola
How do you find the vertex in vertex form? y = a(x-h)²+k (h,k) is the vertex
How do you find the line of symmetry from root form? y = a(x-r₁)(x-r₂) x=(r₁+r₂)/2. Find the average of the two roots.
How do you find the vertex from root form? y = a(x-r₁)(x-r₂) ( (r₁+r₂)/2 , f((r₁+r₂)/2) ) Find the average of the two roots to find the x value. Then put that value back into the equation to find the y value.
How do you find the line of symmetry from standard form? y = ax²+bx+c x = -b /2a
How do you find the vertex from standard form? y = ax²+bx+c ( x = -b /2a, f(x = -b /2a) ). Find the x value using the formula, then put it back into the equation to find the y value.
Created by: meminot
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