How do you graph ax 2 bx c

For now, remember that you would solve for the x-intercepts by substituting 0 in for y and solving for x, as you would for any equation. We would solve for the values of x using the quadratic formula. If you know the quadratic formula, go ahead and solve for the x-intercepts. If you don't know the quadratic formula, not to worry, you're not supposed to! We'll come back to this equation in detail in the next lesson.

What about the vertex? You can't really tell the exact value of the vertex just by looking at the graph. But what is the vertex exactly? The vertex is an important coordinate to find because we know that the graph of the parabola is symmetric with respect to the vertical line passing through the vertex. In this equation, "b" is the coefficient of the x-term and "a", like always, is the coefficient of the x 2 term. Now, all we need to do is to find the y-value. Practice graphing the equation by plotting the vertex and the y-intercept as shown below.

You may want to plot other points, also. Remember, you can pick any number to substitute in the equation for x and solve for y, and the corresponding point will be on the graph. So, plot the vertex, the y-intercept 0, 2. So, another point on this graph is 1, 6.

Also, another point is 2, In most of the previous examples, the parabola opened upward. One of the general characteristics of a parabola is that if the value of "a" which is the coefficient of the x 2 term is negative, the parabola will open downward.

If the value of "a" is positive, the parabola will open upward. So, if you are graphing a parabola and it has "- a" for the x 2 coefficient, and the graph ends up opening upward, you know that you must be graphing incorrectly! This is no problem, just check your calculations. Knowing the characteristics of the graph before you start graphing is a great checking devise!

On the other hand, if "a" is negative, the graph opens downward and the vertex is the maximum value. In this equation, when we substitute values in for x and solve for y, we just square x as we did above.

Then you may graph. On the next slide we will find the y coordinate. We will do this by going to slide 6. The formula it gives us is 0, c , so our y-intercept is 0, The colors that are in parenthesis are the colors the dots or lines will be. Hint: The y intercept will be mirrored exactly due to the need of symmetry. Total views 11, On Slideshare 0. From embeds 0. Number of embeds Downloads Shares 0.

Comments 0. Likes 1. Check by inserting your answer in the original equation. How do you solve system of equations? Follow the steps to solve the problem. Step 1: Multiply the entire first equation by 2. Step 2: Rewrite the system of equations, replacing the first equation with the new equation. Step 3: Add the equations.

Step 4: Solve for x. Step 5: Find the y-value by substituting in 3 for x in either equation. How much is closing cost usually? Is ATM tanked still in business? The y -intercept of any graph is a point on the y -axis and therefore has x -coordinate 0. We can use this fact to find the y -intercepts by simply plugging 0 for x in the original equation and simplifying.

So the y -intercept of any parabola is always at 0,c.