How do you solve the quadratic equation $$x^2 + 13x + 36 = 0$$ ?

Factoring gives $$(x + 9)(x + 4) = 0$$ . Thus, the solutions are $$x = -9$$ and $$x = -4$$ .

What is the solution to the equation $$y = -x^2 - 5x + 12$$ using the quadratic formula?

Using the quadratic formula, the solutions are $$x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(-1)(12)}}{2(-1)}$$ .

How do you find the solutions to the equation $$t^2 + 4t = 2$$ ?

Rearranging gives $$t^2 + 4t - 2 = 0$$ . Using the quadratic formula, the solutions are $$t = -2 \pm \sqrt{6}$$ .

Identify the values of a, b, and c in the equation $$4x^2 - 8x = 3$$ .

Rearranging gives $$4x^2 - 8x - 3 = 0$$ . Thus, a = 4, b = -8, c = -3.

What is the vertex form of a quadratic function?

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

What is the axis of symmetry for a quadratic function?

The axis of symmetry for a quadratic function in standard form $$y = ax^2 + bx + c$$ is given by the line $$x = -\frac{b}{2a}$$ .

How do you determine if a quadratic opens upwards or downwards?

A quadratic opens upwards if the coefficient a > 0 and downwards if a

What is the significance of the y-intercept in a quadratic function?

The y-intercept of a quadratic function is the point where the graph intersects the y-axis, found by evaluating the function at x = 0, which gives $$c$$ in the standard form $$y = ax^2 + bx + c$$ .

How can you graph a quadratic function?

To graph a quadratic function, find the vertex, axis of symmetry, y-intercept, and plot additional points. Then, draw a smooth curve through the points.

Building and Solving Quadratics 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 does the discriminant of a quadratic equation tell us?

Back

4.

FLASHCARD QUESTION

Front

How do you find the vertex of a quadratic function?

Back

5.

FLASHCARD QUESTION

Front

What is the quadratic formula?

Back

6.

FLASHCARD QUESTION

Front

What is the area of a rectangle if the length is 6 meters more than the width and the area is 72 square meters?

Back

7.

FLASHCARD QUESTION

Front

Back

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