Quadratic Functions
quadratic function
A function of the form y = ax^2 + bx + c, where a does not equal 0. The graph of a quadratic function is a parabola, a U-shaped curve that opens up or down.
axis of symmetry
A line that divides a plane figure or a graph into two congruent reflected halves
solving a quadratic
Determining the places where the quadratic crosses the x-axis (or where y = 0)
parabola
Every quadratic function has U-shaped graph called a ______
End behavior of a function even function
For all even degree functions: -when a is positive, the ends are up↑, up↑ -when a is negative, the ends are down↓, down↓
End behavior of a function odd function
For all odd degree functions: -when a is positive, the ends are down↓, up↑ -when a is negative, the ends are up↑, down↓
a is negative
If the graph opens down...
up, down
a tells us if the parabola opens __ or ____
minimum, maximum
a tells us if the vertex is a _______ or _________
standard form
ax^2 + bx + c = 0
opens down
if the leading coefficient (a) is negative, the parabola
opens up
if the leading coefficient (a) is positive, the parabola
parabola
the graph made by a quadratic function
axis of symmetry
the line passing through the vertex that divides the parabola into two symmetric parts called the _____ __ ________
For a quadratic function in standard form, y=ax2+bx+c , the axis of symmetry is a vertical line x=−b2a .
x=-b²a
Axis of Symmetry: x = -9
y = -x² - 18x - 75
Axis of Symmetry: x = -8
y = x² + 16x + 71
Vertex: (6,10)
y = x² - 12x + 46
quadratic formula
The formula used to find the solutions of the quadratic equation ax^2+bx+c = 0 when a,b,and c are real numbers and a isn't equal to zero
factorization
The resolution of a polynomial into factors such that when multiplied together they give the polynomial.
standard form of a quadratic
The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a ≠ 0.
vertex form of quadratic
The vertex form of a quadratic function is f(x) = a(x-h)^2+k, , where a ≠ 0 and (h,k) is the vertex.
