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Any quadratic expression describes a parabola. We can find the exact details of it by observing and manipulating the equation:
y = x2 + 5x - 4
The fact that the squared term has a positive coefficient tells us that the parabola extends infintely upwards on a graph.
To find the bottom most point on the parabola, we can take it's derivative and solve for 0:
dy/dx = 2x + 5
0 = 2x + 5
x = -5/2
The y-coordinate can be found by plugging that value into the original equation:
y = (-5/2)2 + 5(-5/2) - 4
y = 25/4 - 25/2 - 4
y = -25/4 - 16/4
y = -41/4
If you want to find where it intersects the x-axis, you can do so by solving the original equation for zero:
y = x2 + 5x - 4
x2 + 5x - 4 = 0
x2 + 5x + (5/2)2 = 4 + (5/2)2
(x + 5/2)2 = 4 + 25/4
x + 5/2 = ±√[(16 + 25)/4]
x = -5/2 ±√41 / 2
x = (-5 ± √41) / 2
If you want to find another pair of points on the graph, allowing you to roughly sketch the parabola in question, you can do so by assigning another value to y and solving it for x. As long as the result doesn't give you any complex numbers, then you can plot it on the graph giving you a fourth and fifth point with which to plot.
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What is the effect on the graph of the equation y equals x2 plus 2 when it is changed to y equals x2 - 4?
the graph is moved down 6 units
How do you graph y equals x2?
The graph is a parabola facing (opening) upwards with the vertex at the origin.
Is y equals x2 a function?
Y=X^2 is a function for it forms a parabola on a graph.
How does the graph of y equals x2 differ from the graph of y equals x2-4?
Assuming you meant y=x2 & y=x2-4 They are both straight-line graphs, however - they produce different results. Using the values of 1,2,3,4 & 5 for x (as an example)... In the first equation, the value of y would be 1,4,8,16 & 25 In the second equation, y would be -3,0,4,12 & 21
How many x intercepts does the graph of y equals x2 have?
One. It is a double root.
What describes the translation of the graph of y equals x2 to obtain the graph of y equals -x2 - 3?
No translation will invert a quadratic graph.
What is the effect on the graph of the equation y equals x2 plus 2 when it is changed to y equals x2 - 4?
the graph is moved down 6 units
What is the transformation of the graph of y equals x2 to obtain the graph of y equals -x2 plus 3?
First, reflect the graph of y = x² in the x-axis (line y = 0) to obtain the graph of y = -x²; then second, shift it 3 units up to obtain the graph of y = -x² + 3.
What is the graph of y equals x2-7?
9
How do you graph y equals x2?
The graph is a parabola facing (opening) upwards with the vertex at the origin.
Is y equals x2 a function?
Y=X^2 is a function for it forms a parabola on a graph.
Y equals x2 plus 4 lies on which axis?
y = x2 + 4 The graph is a parabola, with its nose at y=4 on the y-axis, and opening upward.
How does the graph of y equals x2 differ from the graph of y equals x2-4?
Assuming you meant y=x2 & y=x2-4 They are both straight-line graphs, however - they produce different results. Using the values of 1,2,3,4 & 5 for x (as an example)... In the first equation, the value of y would be 1,4,8,16 & 25 In the second equation, y would be -3,0,4,12 & 21
How many x intercepts does the graph of y equals x2 have?
One. It is a double root.
What point on y equals x2 is the tangent line parallel to y equals x?
That's true at the point (0.5, 0.25) where the slope of the graph is ' 1 ' .
What is graph of the function y equals X2?
It looks like a parabola which looks like a U shape.
How does the shape of y equals x2 differs from the graph of y equals x3?
y = x2 is an (approximately) U shaped graph that is entirely above the x axis and is symmetric about the y axis. y = x3 is asymptotically negatively infinite when x is negatively infinite and positively infinite when x is positively infinite. It is symmetric about the line x+y=0.
