24 Jun If the question is to sketch the parabola you plot the verte
If the question is to sketch the parabola you plot the vertex and the ##x##- and ##y##-intercepts and draw a smooth line through them. Warning! This is a long answer. ##x= y^2 -4y +3## Note that ##x## is the dependent variable and ##y## is the independent variable. We are going to get a sideways parabola. Step 1. Define your variables. The standard form for the equation of this parabola is ##x = ay^2 +by +c## So ##a= 1## ##b = -4## and ##c = 3## Step 2. Calculate and plot the vertex. The vertex of the curve is given by ##y = -b/(2a) = -(-4)/(21) = -(-2) = 2## Calculate the x-coordinate of the vertex. ##x= y^2 -4y +3 = (2)^2 -4(2) + 3 = 4 -8 + 3 = -1## So the vertex is at (##-12##). Plot your vertex point. Step 3. Find the direction of the opening. The parabola will be a sideways U opening either to the right (####) or to the left (####). Since the coefficient ##a## is positive the parabola opens in the positive direction (to the right). Step 4. (optional) Draw the parabola’s axis of symmetry. A parabola’s axis of symmetry is a line that runs through its middle and divides it in half. For a quadratic of the form ##x = ay^2 +by +c## the axis is a line that passes through the vertex and is parallel to the ##y## axis. For our parabola the axis is the line y = 2. It’s not part of the parabola itself but lightly marking this line on your graph can help you see how the parabola curves symmetrically. Step 5. Calculate and plot the ##x##-intercept. ##x= y^2 -4y +3 = (0)^2 -4(0)+3 = 0 0 + 3 = 3## The ##x##-intercept is at (##30##). Plot this point. Step 6. Calculate and plot any ##y##-intercepts. ##f(y) = y^2 -4y +3 = 0## ##(y-3)(y-1) = 0## ##y-3 = 0## or ##y-1 = 0## ##y = 3## or ##y = 1## The x-intercepts are at (##03##) and (##01##). Add these points to the graph. Step 7. Add any extra points to the graph. The ##x##-intercept at (##30##) is 2 units below the axis. There should be a corresponding point 2 units above the axis at (##34##). Plot this point. Step 7. Draw a smooth parabola passing through all the points.
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