Most likely you have an equation of a parabola. The vertex of a parabola is the location where it changes from going down, to going up (a simplified explanation). Most parabolas that we think of are oriented up or down (the axis is parallel to the y axis), but they could be oriented sideways, or even at an angle. To calculate the vertex of a parabola ususally means to find the coordinates of the vertex.
x - 3.5y + 32 + 5 is an expression, not an equation. Furthermore, even if it were an equation, it has no quadratic term so it could not refer to a parabola. Please check you information and re-enter the question correctly.
There are infinitely many equations; 4 possibilities are: y = x² - 21 y = 29 - x² x = y² - 21 x = 11 - y² Given the focus as well would give an exact equation.
Quadratic equations always have 2 solutions. The solutions may be 2 real numbers (think of a parabola crossing the x axis at 2 different points) or it could have a "double root" real solution (think of a parabola just touching the x-axis at its vertex), or it can have complex roots (which will be complex conjugates of each other). For the last scenario, the graph of the parabola will not touch the x axis.
A quadratic equation could be used to find the optimal ingredients for a mixture. Example: if you are trying to create a super cleanser, you could make a parabola of your ingredients, finding the roots of the equation to find the optimal amount for each ingredient.
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2
Go study
Most likely you have an equation of a parabola. The vertex of a parabola is the location where it changes from going down, to going up (a simplified explanation). Most parabolas that we think of are oriented up or down (the axis is parallel to the y axis), but they could be oriented sideways, or even at an angle. To calculate the vertex of a parabola ususally means to find the coordinates of the vertex.
7
9
6
you didn't put any equations, but the answer probably begins with y= (x-4)^2+1
x - 3.5y + 32 + 5 is an expression, not an equation. Furthermore, even if it were an equation, it has no quadratic term so it could not refer to a parabola. Please check you information and re-enter the question correctly.
There are infinitely many such parabolas, four possibilities are: y = x² - 3 y = 5 - x² x = y² - 3 x = -1 - y² Given the focus as well would give an exact equation
There are infinitely many equations; 4 possibilities are: y = x² - 21 y = 29 - x² x = y² - 21 x = 11 - y² Given the focus as well would give an exact equation.
Quadratic equations always have 2 solutions. The solutions may be 2 real numbers (think of a parabola crossing the x axis at 2 different points) or it could have a "double root" real solution (think of a parabola just touching the x-axis at its vertex), or it can have complex roots (which will be complex conjugates of each other). For the last scenario, the graph of the parabola will not touch the x axis.