0
I may only be in 8th grade but I am absolutely positive that all quadratic equations have 2 solutions.
No - They may have 0,1, or 2 answers
For example, the problem x^2 + 8x +16 = 0 has only one solution -4.
This is because the radical evaluates to 0 rendering the +/- sign irrelevant.
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How do you write quadratic equations using roots?
If the two roots are x = r1 and x = r2 then the quadratic equation is: (x - r1)(x - r2) = x2 - (r1 + r2)x + r1r2 = 0
Systems of equations with different slopes and different y-intercepts have no solutions?
No the only time that a system of equations would have no solutions is when the two equations have the same slope but different y-intercepts which would mean that they are parallel lines. However, if they have different slopes and different y-intercepts than the solution would be where the two lines intersect.
How do you find maximum height when working with quadratic equations?
In a quadratic equation, the vertex (which will be the maximum value of a negative quadratic and the minimum value of a positive quadratic) is in the exact center of any two x values whose corresponding y values are equal. So, you'd start by solving for x, given any y value in the function's range. Then, you'd solve for y where x equals the middle value of the two x's given in the previous. For example:y = x24 = x2x = 2, -2y = (0)2y = 0Which is, indeed, the vertex of y = x2
How do you determine the number of real solutions to a quadratic equation?
Put the equation in the form ax2 + bx + c = 0. Replace a, b, and c in the quadratic formula: x = (-b (plus-or-minus) root(b2 - 4ac)) / 2a. Look at the term under the radical sign, which I wrote as "root" here. If b2 - 4ac is...Positive: the equation has two real solutions.Zero: the equation has one ("double") solution.Negative: the equation has two complex solutions (and therefore no real solution).
Always use the vertex and at least points to graph each quadratic equation?
You should always use the vertex and at least two points to graph each quadratic equation. A good choice for two points are the intercepts of the quadratic equation.
