Solving Systems of Linear and Quadratic Equations

Set them equal to each other

Simplify into '= 0' format (like a standard Quadratic Equation)

Solve the Quadratic Equation

The matching y values are (also see Graph)

What about a system of two equations where one equation is linear, and the other is quadratic

Remember that the slope-intercept form of the equation for a line is y=mx+b , an______ the stan______ar______ form of the equation for a parabola with a vertical axis of symmetry is y=a x^2 +bx+c,  a≠0. To avoi______ confusion with the variables, let us write the linear equation as y=mx+______  where m is the slope an______ ______ is the y-intercept of the line.

We can use a version of the ______ method to solve systems of this type.

To avoid confusion with the variables, let us write the linear equation as y=______  where m is the slope and d is the y-intercept of the line. Substitute the expression for y from the linear equation, in the quadratic equation. That is, substitute ______  for y in y=a x^2 +bx+c.

Now, rewrite the new quadratic equation in standard form. Subtract mx+d  from both sides. ( mx+d )−( mx+d )=( a x^2 +bx+c )−( mx+d ) 0=______

Now we have a quadratic equation in one variable, the solution of which can be found using the quadratic formula. The solutions to the equation a x^2 +(b−m)x+(c−d)=0   will give the ______ of the points of intersection of the graphs of the line and the parabola. The corresponding y-coordinates can be found using the linear equation.

Another way of solving the system is to ______ the two functions on the same coordinate plane and identify the points of intersection.

A similar method can be used to find the intersection points of a line and a ______ or a line and an ellipse.

Don't let the term 'imaginary' get in your way - there is nothing imaginary about them. They are just extensions of the ______ numbers, just like rational numbers (fractions) are an extension of the integers.

The name 'imaginary number' was coined in the 17th century as a derogatory term, as such numbers were regarded by some as fictitious or useless. The term 'imaginary number' now means simply a ______ number with a real part equal to 0, that is, a number of the form bi.

The term 'imaginary number' now means simply a complex number with a real part equal to 0, that is, a number of the form ______.

The Real Numbers did not have a name before ______.