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Practice Quiz #2 - CTS Name: nirections: Find the vertex, x-intercepts, and y-intercepts for each equation. If it can be factored, solve it that way. If it can't be factored, solve it by completing the square (vertex form). Then, use the information to graph. 1. 2. -z Vertex: X-intercepts: and y-intercept: -z Y = 6x2 - 23x 7 ) Vertex: X ... Dollar tree store manager salary california
16. y = 3x2 - +2 This parabola has a (max or min It also has a (vertex, -intercept or x-intercept) at ( Q, L) Convert the following functions to another form in order to determine the given characteristic.

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Examples: Write a quadratic equation or function in Vertex Form: f (x) — y = a(x— +k If you know the vertex of a parabola, (h,k) , then you still need at least one other point on the parabola in order to write an equation. Use the vertex form and fill in all the information you have. Then use the point on the parabola and substitute in for ...

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12. Find an equation of the line that passes through (2, -1) and is perpendicular to the line 2x + 7y = 5. 1 . Find the domain of the function. 2x-1 2X+1 14. Write in the form y = a(x— + k: y 3x2 +12x+17. (Complete the square.) 15. The graph of the function f (x) = ax 2 + hr + c has a vertex at (3, —2) and passes through (6, 25). Find a,b ...

-3x2+12x-1 = y Solve the quadratic equation when y = 0 by means of the quadratic equation formula which gives x values of 3.914854216 and 0.085145784.

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quadratic equation has a term term Axis of Symmetry: Vertex: vhere 0 term , and a 3 a ka 0-5 a Gus a KeyCcncept GraphofaQuadratic Considerthegraph bX+ c, where 0, Words They-interceptis 1(0) + c. Thegquationofthe axisof symmetnt isž= The x-coordinateofthevettexis Ex. 2 Graph fCx) + 4xo b : x = -b - 2(1) Ex. 2c: Grap y=3x2 y-ïntertžpt: c Of

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a) In standard form with y-int (0, —5) d) y = 2x2 — 12x = 2.X(X -G) v.u-k-x x -3 b) In vertex form with vertex (7,3) d) In vertex form with vertex (—2,0) focus c) In form with zeros (3,0) & (—8,0) 12. Write an equation of each parabola shown. focus v r ex (op 8 x

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Expanding the exponent, distributing, and simplifying is how you can simplify Vertex form —Y Standard form Convert the following vertex form equations to standard form: 9. f(x) factoring!) 3x2+ I 12. f(x) 4x2+16x+ 15 15. f(x) 8. f(x) — 1)2+ 4 Convert the following standard form equations to factored form (aka.. —x2— 12x — 35 ll.f(x ...

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Standard form: ax2 + bx + c; a, b, c E IR, a O where a is the vertical stretch parameter and c is the y-intercept. Vertex form: y = a(x — + q, where vertex = (p,q) and a is vertical stretch "Completing the square" is an important step when rewriting quadratic functions from standard form to vertex form; it is how we get (x — p)

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The vertex form of y=-3x^2+12x-8 is y=-3(x-2)^2+4 To derive vertex form y=a(x-h)^2+k from general quadratic form y=ax^2+bx+c, you can use completing the square y=-3x^2+12x-8 = -3 (x^2-4x+8/3) = -3 (x^2-4x +(-2)^2-(-2)^2 +8/3) = -3 ((x-2)^2 -4+8/3) = -3 ((x-2)^2 -4/3) = -3 (x-2)^2 -4