How do you solve $$3 + 9r^2 = 12$$ using the Square Root Property?

Subtract 3 from both sides: $$9r^2 = 9$$ . Then divide by 9: $$r^2 = 1$$ . Finally, take the square root: $$r = ±1$$ .

What are the solutions to $$5x^2 + 130 = 5$$ ?

First, simplify to $$5x^2 = -125$$ , then $$x^2 = -25$$ . The solutions are $$x = 5i$$ and $$x = -5i$$ .

How do you solve $$x^2 + 64 = 0$$ using the Square Root Property?

Rearranging gives $$x^2 = -64$$ . The solutions are $$x = 8i$$ and $$x = -8i$$ .

What is the solution to the equation $$(x-3)^2 = -20$$ ?

Rearranging gives $$(x-3)^2 = 20$$ . Taking the square root gives $$x - 3 = ±2i√5$$ , so $$x = 3 ± 2i√5$$ .

What are the solutions to $$(x - 3)^2 = 25$$ ?

Taking the square root gives $$x - 3 = ±5$$ . Thus, the solutions are $$x = 8$$ and $$x = -2$$ .

What is the discriminant in a quadratic equation?

The discriminant is the part of the quadratic formula under the square root: $$b^2 - 4ac$$ . It determines the nature of the roots.

How do you determine if a quadratic equation has two distinct real solutions?

If the discriminant is greater than zero (b^2 - 4ac > 0), the equation has two distinct real solutions.

What is the general form of a quadratic equation?

The general form is $$ax^2 + bx + c = 0$$ , where a, b, and c are constants and $$a ≠ 0$$ .

What is the vertex form of a quadratic equation?

The vertex form is $$y = a(x - h)^2 + k$$ , where (h, k) is the vertex of the parabola.

What is the axis of symmetry in a quadratic function?

The axis of symmetry is the vertical line that divides the parabola into two mirror images, given by $$x = -\frac{b}{2a}$$ .

How can you check your solutions to a quadratic equation?

You can substitute the solutions back into the original equation to verify that both sides are equal.

What is the significance of the square root in solving quadratic equations?

The square root allows us to find both positive and negative solutions, which is essential for solving equations of the form $$x^2 = k$$ .

Flashcard

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Mathematics

•

9th Grade

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Practice Problem

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Hard

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FLASHCARD QUESTION

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What is the Square Root Property?

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FLASHCARD QUESTION

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FLASHCARD QUESTION

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FLASHCARD QUESTION

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Back

FLASHCARD QUESTION

Front

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FLASHCARD QUESTION

Front

Back

FLASHCARD QUESTION

Front

What does it mean if a quadratic equation has no real solutions?

Back

It means that the discriminant (b^2 - 4ac) is less than zero, indicating that the solutions are complex numbers.

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