Speed:
This algebra 1 math tutorial from NutshellMath offers targeted homework help with graphing quadratic functions. The instruction is focused on homework problems 11-13 and 23-31 from pages 520 and 521 of the Algebra 1 text from Prentice Hall.
Quadratic functions are equations expressed as polynomials of the second degree. Such functions have graphs that are parabolas; symmetric, non-uniform curves with a single peak or valley, the center of which is called the vertex. Homework problems covered by this tutorial involve finding the key elements of the parabola in order to simply graph quadratic functions.
The first step in graphing quadratic functions is to get the equation of the function into standard quadratic form. This standard form is: y=ax^2+bx+c, where a, b, and c are constant coefficients. Using this form, it is possible to find the axis of symmetry, the vertex, and other points of the parabola. The axis of symmetry, or the vertical line through which the vertex crosses and which splits the parabola evenly in half, is the line x=(-b)/(2a). Using this axis is possible to find the vertex of the parabola. By plugging in (-b)/(2a) as a value for x into the quadratic function, the output value for y will be the y coordinate of the vertex. The coefficient 'a' also can be used to figure out if the parabola opens up or down. If 'a' is negative, the curve will slope down from the vertex, opening down. If 'a' is positive, then the curve will open upward, and the vertex will be the lowest point of the parabola.
Knowing the vertex, it is possible to then graph the parabola. One method of graphing is to plot the vertex, and then make a table of x-values and solving for the corresponding y-values using the function, as with a linear equation. Plot several points, and then sketch the curve of the parabola.
Learning to graph parabolas is helpful in many situations in algebra. It is possible to use the graph of a parabola to find the roots of the corresponding quadratic equation, by checking where the parabola intersects the x-axis. It is also possible to use parabolas to model situations in other fields.
This algebra 1 math tutorial from NutshellMath offers targeted homework help with graphing quadratic functions. The instruction is focused on homework problems 11-13 and 23-31 from pages 520 and 521 of the Algebra 1 text from Prentice Hall.
Quadratic functions are equations expressed as polynomials of the second degree. Such functions have graphs that are parabolas; symmetric, non-uniform curves with a single peak or valley, the center of which is called the vertex. Homework problems covered by this tutorial involve finding the key elements of the parabola in order to simply graph quadratic functions.
The first step in graphing quadratic functions is to get the equation of the function into standard quadratic form. This standard form is: y=ax^2+bx+c, where a, b, and c are constant coefficients. Using this form, it is possible to find the axis of symmetry, the vertex, and other points of the parabola. The axis of symmetry, or the vertical line through which the vertex crosses and which splits the parabola evenly in half, is the line x=(-b)/(2a). Using this axis is possible to find the vertex of the parabola. By plugging in (-b)/(2a) as a value for x into the quadratic function, the output value for y will be the y coordinate of the vertex. The coefficient 'a' also can be used to figure out if the parabola opens up or down. If 'a' is negative, the curve will slope down from the vertex, opening down. If 'a' is positive, then the curve will open upward, and the vertex will be the lowest point of the parabola.
Knowing the vertex, it is possible to then graph the parabola. One method of graphing is to plot the vertex, and then make a table of x-values and solving for the corresponding y-values using the function, as with a linear equation. Plot several points, and then sketch the curve of the parabola.
Learning to graph parabolas is helpful in many situations in algebra. It is possible to use the graph of a parabola to find the roots of the corresponding quadratic equation, by checking where the parabola intersects the x-axis. It is also possible to use parabolas to model situations in other fields.