Which is the graph of a quadratic equation that has a positive discriminant?

How do you tell if a graph has a positive discriminant?

A positive discriminant indicates that the quadratic has two distinct real number solutions. A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions are real numbers.

How can you use the discriminant when you are graphing a quadratic function?

You can use the discriminant, b2 4ac, to find the number of solutions of a quadratic equation in the standard form ax2 bx c 0. A positive value indicates two solutions, zero indicates one solution, and a negative value indicates no real solution.

Which graph shows a quadratic function with a discriminant value of 0?

Which graph shows a quadratic function with a discriminant value of 0? On a coordinate plane, a parabola opens up.

Is the discriminant negative or positive?

A quadratic expression which always takes positive values is called positive definite, while one which always takes negative values is called negative definite. Quadratics of either type never take the value 0, and so their discriminant is negative.

What can the discriminant tell you?

The discriminant tells you how many solutions there are to quadratic equation or how many x intercepts there are for a parabola. If the discriminant is less than zero, there are no solutions and if the discriminant is equal to zero, there is one solution.

How many solutions does a quadratic equation have if it’s discriminant is zero?

The discriminant is the part under the square root in the quadratic formula, b²-4ac. If it is more than 0, the equation has two real solutions. If it’s less than 0, there are no solutions. If it’s equal to 0, there is one solution.

How do you use the discriminant?

NotesThe quadratic equation we’re working with is x2-2x+3=0. The discriminant comes from the Quadratic Formula. Remember, the discriminant tells us how many and what type of solutions a quadratic equation has. Remember, the discriminant is equal to b2-4ac. The standard form of a quadratic equation is ax2+bx+c=0.

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What is a repeated real number solution?

When the left side factors into two linear equations with the same solution, the quadratic equation is said to have a repeated solution. We also call this solution a root of multiplicity 2, or a double root. SOLVING BY THE SQUARE.

How do you find the discriminant on a calculator?

ax2 + bx + c = 0 The discriminant calculator is an online calculator tool, which calculates the discriminant of a given quadratic equation. For a quadratic equation ax2 + bx + c = 0, where a ≠ 0, the formula of discriminant is b2 – 4ac. ◾ Number of roots – whether the quadratic equation has two roots, one root or none.

What does the quadratic formula tell you about the graph of a quadratic function?

So, given a quadratic function, y = ax2 + bx + c, when “a” is positive, the parabola opens upward and the vertex is the minimum value. On the other hand, if “a” is negative, the graph opens downward and the vertex is the maximum value.

How do I find the discriminant of a parabola?

Quadratic EquationsThe number D = b2 – 4ac is called “discriminant”. If D < 0, then the quadratic equation has no real solutions(it has 2 complex solutions). The vertex of the parabola is x = − b 2 a displaystyle x = -frac{b}{2a} x=−2ab.Problem 3. Solve the equation: Problem 4. Solve the equation:

When solving a quadratic equation What is the difference between a root and a solution?

Zeros (roots) of a function are the values of x for which f(x)=0 while solutions are the values of the x which make the equation f(x) = c true where c is any constant . for example if f(a) = 0 then a is called root and (a,0) called solution of f(x) while if f(b) = c then (b,c) is called solution.

What happens if the discriminant is less than 0?

If the discriminant of a quadratic function is less than zero, that function has no real roots, and the parabola it represents does not intersect the x-axis.

How many solutions if the discriminant is negative?

If the value of the discriminant is zero, the quadratic equation has one real solution. If the value of the discriminant is negative, the quadratic equation has no real solutions.

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