What is the slope of a line perpendicular to the line represented by the equation $$y=-\frac{2}{7}x-5$$ ?

The slope of a line perpendicular to $$y=-\frac{2}{7}x-5$$ is the negative reciprocal of -\frac{2}{7}, which is $$\frac{7}{2}$$ .

What are the steps to solve the equation $$9x^2-2x=3$$ ?

1. Rearrange the equation to standard form: $$9x^2-2x-3=0$$ . 2. Use the quadratic formula $$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$$ where a=9, b=-2, c=-3.

Convert the quadratic function $$y=-4(x+4)^2+2$$ to standard form.

Expand the equation: $$y=-4(x^2+8x+16)+2 = -4x^2-32x-64+2 = -4x^2-32x-62$$ .

What is the vertex of a parabola in standard form $$y=ax^2+bx+c$$ ?

The vertex can be found using the formula $$x = -\frac{b}{2a}$$ to find the x-coordinate, then substitute back to find the y-coordinate.

What is the definition of a quadratic function?

A quadratic function is a polynomial function of degree 2, typically in the form $$y=ax^2+bx+c$$ where $$a\neq0$$ .

What is the significance of the discriminant in a quadratic equation?

The discriminant, given by $$b^2-4ac$$ , determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, no real roots.

What is a direct variation?

Direct variation describes a relationship where one variable is a constant multiple of another, expressed as $$y=kx$$ where $$k$$ is a non-zero constant.

How do you determine if a point lies on a line represented by an equation?

Substitute the x-coordinate of the point into the equation and see if the resulting y-coordinate matches the y-coordinate of the point.

What is the formula for the slope of a line given two points (x1, y1) and (x2, y2)?

The slope $$m$$ is calculated as $$m = \frac{y2 - y1}{x2 - x1}$$ .

What does it mean for two lines to be perpendicular?

Two lines are perpendicular if the product of their slopes is -1.

What is the standard form of a quadratic equation?

The standard form of a quadratic equation is $$ax^2 + bx + c = 0$$ where $$a, b, c$$ are constants and $$a\neq0$$ .

What is a zero of a function?

A zero of a function is a value of $$x$$ that makes the function equal to zero, indicating where the graph intersects the x-axis.

Algebra 1 STAAR Review (#2) Flashcards

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15 questions

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1.

FLASHCARD QUESTION

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2.

FLASHCARD QUESTION

Front

If Jon pays $8.75 for 5 gallons of gas, how do you find the cost for 32 gallons?

Back

To find the cost for 32 gallons, use the direct variation formula: Cost = (Cost per gallon) * (Number of gallons). First, find the cost per gallon: $8.75 / 5 = $1.75. Then, multiply by 32: $1.75 * 32 = $56.

3.

FLASHCARD QUESTION

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Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

What does it mean if a graph has a maximum value?

Back

A maximum value means the highest point on the graph, indicating the greatest output value of the function.

6.

FLASHCARD QUESTION

Front

How do you find the y-intercept of a function?

Back

7.

FLASHCARD QUESTION

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Back

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