Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 13, 2024

Find the y-intercept of the parabola $y=x^2 + 6x + \frac{19}{4}$ . Simplify the answer as a fraction or integer.

STEP 1

Assumptions
1. The equation of the parabola is $y = x^2 + 6x + \frac{19}{4}$ .
2. To find the $y$ -intercept of the parabola, we need to find the value of $y$ when $x = 0$ .

STEP 2

The $y$ -intercept occurs where the parabola crosses the $y$ -axis. This happens when $x = 0$ .

STEP 3

Substitute $x = 0$ into the equation of the parabola to find the $y$ -intercept.
$y = (0)^2 + 6(0) + \frac{19}{4}$

STEP 4

Simplify the equation by performing the operations.
$y = 0 + 0 + \frac{19}{4}$

STEP 5

The result gives us the $y$ -intercept.
$y = \frac{19}{4}$
The $y$ -intercept of the parabola $y = x^2 + 6x + \frac{19}{4}$ is $\frac{19}{4}$ .

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