Vocabulary
quadratic function- a function that can be written in standard form y=ax^2+bx+c where a does not equal zero.
parabola- the graph of a quadratic function.
vertex- the lowest or highest point on a parabola.
axis of symmetry- divides the parabola into mirror images and passes through the vertex.
minimum value- the y-coordinate of the vertex for y=ax^2+bx+c when a>0.
maximum value- the y-coordinate of the vertex for y=ax^2+bx+c when a<0.
parabola- the graph of a quadratic function.
vertex- the lowest or highest point on a parabola.
axis of symmetry- divides the parabola into mirror images and passes through the vertex.
minimum value- the y-coordinate of the vertex for y=ax^2+bx+c when a>0.
maximum value- the y-coordinate of the vertex for y=ax^2+bx+c when a<0.
Essential Information
Parent Function for Quadratic Functions
the parent function for the family of all quadratic functions is f(x)=ax^2
any quadratic in which b=0, the axis of symmetry is x=0
the parent function for the family of all quadratic functions is f(x)=ax^2
any quadratic in which b=0, the axis of symmetry is x=0
Properties of the Graph y=ax^2+bx+c
- The graph opens up if a<0 and opens down if a>0.
- the graph is narrower than the graph y=x^2 if ∣a∣>1 and wider if ∣a∣<1.
- the axis of symmetry is x=-b/2a and the vertex has the x-coordinate -b/2a.
- The y-intercept is c. So, the point (0,c) is on the parabola.
Minimum and Maximum Values
The maximum or minimum value for any quadratic function is the maximum or minimum
f(x)=ax^2+bx+c
The maximum or minimum value for any quadratic function is the maximum or minimum
f(x)=ax^2+bx+c
- when a is positive the parabola opens upwards
- when a is negative the parabola opens downwards
Example Graphing:
you can also make a table through plunging in x values and finding their corresponding y values and plotting the points