How do you solve the equation $$5b^2 - 4 = 41$$ ?

First, rearrange to $$5b^2 = 45$$ , then $$b^2 = 9$$ , so $$b = \pm 3$$ .

How do you solve the equation $$9x^2 = 16$$ ?

Rearranging gives $$x^2 = \frac{16}{9}$$ , so $$x = \pm \frac{4}{3}$$ .

What is the vertex form of a quadratic equation?

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

How do you solve the equation $$\left(5x-2\right)^2-3=14$$ ?

First, simplify to $$\left(5x-2\right)^2 = 17$$ , then take the square root and solve for $$x$$ .

What is the axis of symmetry in a quadratic function?

The axis of symmetry is a vertical line given by $$x = -\frac{b}{2a}$$ .

What is the significance of the leading coefficient in a quadratic equation?

The leading coefficient (the value of $$a$$ ) determines the direction of the parabola: if $$a > 0$$ , it opens upwards; if $$a

How do you find the roots of a quadratic equation graphically?

The roots can be found by identifying the x-intercepts of the graph of the quadratic function.

What is the relationship between the roots and coefficients of a quadratic equation?

For a quadratic equation $$ax^2 + bx + c = 0$$ , the sum of the roots is $$-\frac{b}{a}$$ and the product of the roots is $$\frac{c}{a}$$ .

How do you solve the equation $$3x^2 = 12$$ ?

Rearranging gives $$x^2 = 4$$ , so $$x = \pm 2$$ .

A parabola is the graph of a quadratic function, characterized by its U-shape and defined by the equation $$y = ax^2 + bx + c$$ .

Solving Quadratic Equation Flashcard Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a quadratic equation?

Back

2.

FLASHCARD QUESTION

Front

What is the standard form of a quadratic equation?

Back

3.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

4.

FLASHCARD QUESTION

Front

What does the discriminant of a quadratic equation indicate?

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

There is no real number solution because the left side is non-negative and the right side is negative.

7.

FLASHCARD QUESTION

Front

Back

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