Algebra Unit 6
vertex (1, -5) point (3,-1)
y=x^2-2x-4
Find the y-intercept from the quadratic equation.; x^2-y=-4x-3
(0,3)
Steps to solving quadratic equations by factoring:
1. Write the equation in standard quadratic form. 2. Factor a GCF first, if possible, and then factor a trinomial if possible. 3. Use the Zero Product Property. 4. Solve each equation .5. Check your solutions
Straight line
Linear function
What point is the maximum of this parabola?
There is no maximum because the parabola opens upward.
transformation of a function
a change in the size, shape, or position of a function
parabola
a curved line formed from a set of points that are all the same distance from a line, called a directrix, and a point, called a focus
quadratic function (curvy line)
a function in the form f (x)=ax^2+bx+c where a, b, and c are real numbers and a is not equal to 0, that will graph as a parabola
directrix of a parabola
a line perpendicular to the axis of symmetry that lies outside a parabola that helps determine the shape of a parabola
focus of a parabola
a point inside the parabola that helps determine the shape of the curve
dilation of a quadratic function
a transformation of a quadratic function that is represented by a parabola that becomes wider or narrower than the original parabola
translation of a quadratic function
a transformation of a quadratic function that is represented by a parabola that is shifted up, down, left, or right of the original parabola
reflection of a quadratic function
a transformation of a quadratic function that is represented by a parabola that opens the opposite direction of the original parabola
axis of symmetry of a parabola
a vertical line that divides a parabola into two halves that are identical in size and shape, but reversed in direction
Identify the parts of the parabola.
a. vertex b. directrix c. axis of symmetry d. focus
Determine the direction of the parabola by the value of a.; x^2-y=-4x-3
a>0; The parabola will open upward
The ___ is the part of the quadratic formula that determines the number of roots.
discriminant
The quadratic formula allows us to find ___ solutions to any quadratic equation.
exact
zero of a function
for any function, a value for x that causes y to equal 0; the x-value at the coordinate where the graph of a function crosses the x-axis
Constant change in x-values result in similar change in y-values.
linear function
f(x)=ax+b
linear function
A parabola
quadratic function
Constant change in x-value results in y-value decreasing then increasing in value.
quadratic function
f (x)=ax^2+bx+c
quadratic function
Changes in y-value are constant in their second differences.
quadric function
curvy line
quadric function
A quadratic function may have one root, two roots, or no ___ roots.
real
The solutions to a quadratic equation or the zeros of a quadratic function are also called the ___ of the quadratic function.
roots
second difference
the difference in values between the values of the first differences
first differences
the differences in y-values produced by a constant change in x-values in a function
vertex of a parabola
the highest or lowest point on the graph of a quadratic function
discriminant
the part of the quadratic formula that determines the number of roots which are also x-intercepts
roots of a quadratic function
the solutions to a quadratic function; the zeros of a quadratic function
maximum of a quadratic function
the y-value of the coordinate of the vertex of a parabola that opens downward
minimum of a quadratic function
the y-value of the coordinate of the vertex of a parabola that opens upward
What point is the minimum of this parabola?
vertex
Find the vertex by substituting the x-value you found in the previous question into the quadratic equation.; x^2-y=-4x-3
vertex= (-2,-1)
Find the axis of symmetry using the formula x=-b/2a
x=-2
Put the equation in quadratic form; x^2-y=-4x-3
y=x^2+4x+3
