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It is the equation of a quadratic function that happens to factor very nicely:
y = 2x2 + 5x - 3 = (x + 3)(2x - 1).
When the product of two numbers equals zero, then one or other of them must equal zero.
Therefore, when y = 0, one of the two factors must also equal zero:
Hence, either x = -3 or x = ½, when y = 0.
This implies that the graph of this function crosses the x-axis at two places: namely, at (0,-3) and at (0,½).
As the graph of every quadratic function is a parabola, its axis of symmetry is the vertical line passing through the point on the x-axis that is mid-way betwixt the two points named above, where the function crosses the x-axis: namely, at (0,-1¼).
To find the vertex of the above parabola, we solve for y where x = -1¼:
y = (x + 3)(2x - 1)
= (-1¼ + 3)(-1¼ - 1)
= (1¾)(-2¼)
= (7/4)(-9/4) = 63/16 = 3 15/16
-3;
hence, the vertex is located at the point, (-1¼,315/16).
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∙ 12y ago
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Is y equals 3x plus 1 and -2x2 a function?
No.
Is y equals 5x3 plus 6 linear?
y = 5x3 + 6 is a cubic equation, not a linear equation. Linear equations contain only terms of degree 0 (i.e. constants) and terms of degree 1.
What are the roots of the quadratic equation y equals 2x2 plus 3x-20?
2x2 + 3x - 20 = (x + 4)(2x - 5).
Is y equals 2x2 a function?
no
What is y equals 5x3 plus 5?
y = 5x3 + 5 is a cubic equation. You cannot solve for x (or y), because there are two variables and only one equation. If you graph this, however, you will see a curve that passes through all possible points that make this equality true.
Is y equals 3x plus 1 and -2x2 a function?
No.
Is y equals 5x3 plus 6 linear?
y = 5x3 + 6 is a cubic equation, not a linear equation. Linear equations contain only terms of degree 0 (i.e. constants) and terms of degree 1.
What are the roots of the quadratic equation y equals 2x2 plus 3x-20?
2x2 + 3x - 20 = (x + 4)(2x - 5).
Is y equals 2x2 a function?
no
What is the minimum value of the equation y equals 2x2 plus 5?
y=2x2+5. Plug in 0 for x, and you get y=2(0)^2 +5 =0+5=5. 5 is the minimum value for y.
What is y equals 5x3 plus 5?
y = 5x3 + 5 is a cubic equation. You cannot solve for x (or y), because there are two variables and only one equation. If you graph this, however, you will see a curve that passes through all possible points that make this equality true.
When a plane is traveling at the parobola y equals -2x2 plus 10 what is the angle of the descent when x equals 1.5?
1.249 radians from the horizontal.
Y equals 2x plus 5 is a linear equation because?
There are no powers e.g 2x2 would be due to the 2
How do you write y equals 2xsquared plus 4x-7 in function notation?
f(x) = 2x2 + 4x - 7
How many x intercepts are in y equals 2x2 plus 4x plus 3?
None because the discriminant of this quadratic equation is less than zero.
What is the graph of the equation 2x2-6x plus 2y plus 18 equals 0?
2x2-6x+2y+18 = 0. Subtract the 2y from both sides. 2x2-6x+18 = -2y. Divide all by -2 to get y by itself. -x2+3x-9 = y. This graph is going to be a parabola that opens downward, like a frown.
What is the length of the line that spans the parabolas of y equals 4x squared -2x -1 and y equals -2x squared plus 3x plus 5?
If: y = 4x2-2x-1 and y = -2x2+3x+5 Then the length of the line works out as: 65/18 or 3.6111 ... recurring decimal 1
