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# High School: Functions

## Identical Quadratics

Directions: Using the digits 0 to 9 at most one time each, fill in the boxes to create three equations that produce the exact same parabola. Source: Zack Miller

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## Line Builders

Directions: Complete the table & graph below or here on Desmos to create a linear relation. Find the equation of the linear relation. Fill in the table again and again to create as many different linear relations as you can. What do the graphs have in common? What do the equations have in common? Source: Jon Orr

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## Create a Quadratic Equation, Given Constraints

Directions: Write a quadratic equation that has a y-intercept of 24 and the distance between the x-intercepts is 10. Bonus: find more than 2 quadratic equations. Source: Daniel Luevanos

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## Quadratics with Defined Roots in Standard Form

Directions: Create three equations for quadratics in standard form that have roots at 3 and 5. Source: Robert Kaplinsky

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## Quadratics with Defined Roots in Vertex Form

Directions: Create three equations for quadratics in vertex form that have roots at 3 and 5 but have different maximum and/or minimum values. Source: Robert Kaplinsky

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## Angles of a Polygon

Directions: The measures of the angles of a convex polygon form an arithmetic sequence. The smallest angle has a measurement of 129 degrees. The largest angle has a measurement of 159 degrees. Find the number of sides in this polygon. Source: Ricardo Navarro

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## Quadratic Formula

Directions: What are the maximum and minimum values for c if x^2 + 12x + 32 = (x+a) (x+b) + c? Source: Jedidiah Butler

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## Maximum Value of a Quadratic in Vertex Form

Directions: Create a quadratic equation with the greatest possible maximum value using the digits 1 through 9, no more than one time each. Source: Robert Kaplinsky

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## Maximum Value of a Quadratic in Standard Form

Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to create a quadratic equation with the greatest possible maximum value. Source: Robert Kaplinsky

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## Arithmetic vs Geometric

Directions: Which is bigger? The common ratio, r, in a geometric sequence with OR the common difference, d, in an arithmetic sequence with Source: Nanette Johnson

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