Quadratic Equations - Christopher Kamugisha | Library

Instructions

1

Match each of the following vacabulary words with its definition, equation or formula.

Draggable item		Corresponding Item
One real solution		U shaped graph of a quadratic equation.
\|a\| is less than 1 but greater than 0 0<\|a\|<1		The turning point of a parabola, it represents the maximum or minimum point of the parabola.
k is positive		The vertical line parallel to the y-axis that divides the parabola into 2 symetrical halves.
vertex		The place where the parabola corses or intersects with the x-axis.
horizontal translation
Standard form equation
Quadratic formula
parent function		the highest point of the parabola, it happens when a is negative and the parabola opens down.
dilatation		the lowest point of a parabola, it happens when a is positive and the parabola open up.
Equation for the axis of symmetry		the simplest form of a parabola
Complete Quadratic Equation		transformation that stretches (narrows) or compresses (widens) a parabola depending on the absolute value of \|a\|. Stretches if \|a\| > 1 Compresses if 0<\|a\|<1
Two real solutions		transformatoion that reflect the parabola over the x-axis when the value of a is negative.
Axis of Symmetry		transformation that shifts the parabola up or down depending on the value of k. If k is negative the parabola shifts down, if k is positive the parabola shiifts up.
vertical translation		transformation that shifts the parabola left or right depending on the value of h. If h is negative the parabola shifts right, if h is positive the parabola shifts left. Remember that the vaklue of h is opposite in the equation.
\|a\| is greater than 1		Parabola open up
discriminant		Parabola opens down
k is negative		Parabola become narrower (stretches) compared to the parabola of the parent function
Parabola		Parabola becomes wider (compresses) compared to the parabola of the parent function
No real solutions		Vertex of the Parabola shifts up compared to the vertex of the parent function.
vertex form equation		Vertex of the parabola shifts down compared to the vertex of the parent function.
h is negative		Vertex of the parabola shifts left compared to the vertex of the parent function.
minimum		Vertex of the parabola shifts right compared to the vertex of the parent function.
reflection		determines the number of real solutions that a quadratic equations has.
x-intercetpt, solution, roots or zeros		the value of the discriminant is negative.
Incomplete Pure Quadratic Equation		the value of the discriminant is zero.
maximum		the value of the discriminant is positive.
h is positive
a negative		A quadratic equation that only has the quadratic term and the independent or constant term. Both terms ,must be perfect squares and the opperation sign between the terms must be negative.
Incomplete Mixed Quadratic Equation		A quadratic equation that has only the quadratic term and the linear term.
a positive		A quadratic equation that has all three terms, a quadratic term (ax^2), a linear term (bx) and a constant or independent term (c)