Math  /  Algebra

QuestionAssuming all parabolas are of the form y=ax2+bx+cy=a x^{2}+b x+c, drag and drop the graphs to match the appropriate a-value (if necessary). a=1a=0.25a=-1 \quad a=0.25 a=4a=4
Answer Attempt 2 out of 2

Studdy Solution

STEP 1

What is this asking? We need to match parabolas drawn on a graph to their corresponding equations, focusing on how the *a* value affects the parabola's shape. Watch out! Don't mix up upward and downward opening parabolas, and remember how *a* affects the width: bigger *a* means narrower parabola, smaller *a* means wider parabola.

STEP 2

1. Analyze the *a* values
2. Match parabolas to *a* values

STEP 3

Alright, let's break down what these *a* values tell us!
We've got a=1a = -1, a=0.25a = 0.25, and a=4a = 4.
Remember, the *a* value is the coefficient of the x2x^2 term in our parabola equation y=ax2+bx+cy = ax^2 + bx + c.

STEP 4

The sign of *a* tells us whether the parabola opens upwards or downwards.
A **negative** *a* value, like a=1a = -1, means a **downward-opening** parabola, shaped like a frown.
A **positive** *a* value, like a=0.25a = 0.25 and a=4a = 4, means an **upward-opening** parabola, shaped like a smile.

STEP 5

The *magnitude* or absolute value of *a* tells us how **wide** or **narrow** the parabola is.
A **larger** magnitude means a **narrower** parabola.
A **smaller** magnitude means a **wider** parabola.

STEP 6

Let's look at the first graph, a downward-opening parabola.
Since it's opening downwards, we know the *a* value must be negative.
That means this parabola corresponds to a=1a = -1.

STEP 7

Now, we have two upward-opening parabolas and two positive *a* values, a=0.25a = 0.25 and a=4a = 4.
Remember, a larger magnitude of *a* means a narrower parabola.

STEP 8

One parabola is quite wide, and the other is much narrower.
Since 44 is larger than 0.250.25, the narrow parabola corresponds to a=4a = 4, and the wide parabola corresponds to a=0.25a = 0.25.

STEP 9

The first graph (downward-opening) matches a=1a = -1.
The second graph (wide, upward-opening) matches a=0.25a = 0.25.
The third graph (narrow, upward-opening) matches a=4a = 4.

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